Department of Electrical Engineering

Indian Institute of Technology Bombay

Mumbai 400076, India

Telephone:(91)-22-25769405 (O)

Fax:(91)-22-25723707

E-mail: borkar.vs@gmail.com

- Phone (O): +91-22-2576-9405
- Phone (R): +91-22-2576-8405
- E-Mail: borkar[AT]ee.iitb.ac.in
- Homepage

List of Publications

Journal Papers

- A. P. Azad, S. Alouf, E. Altman, V. S. Borkar, G. S. Paschos , "Optimal Control of Sleep Periods for Wireless Terminals", IEEE Journal on Selected Areas in Communications, vol. 29, no. 8, pp. 1605 -1617, 2012.
- V. S. Borkar, "Opportunistic transmission across fading channels: issues and algo-rithms", Proc. NASI A: Phys. Sci., pp. , 2011.
- Nitin Salodkar, Abhay Karandikar, Vivek Borkar, "A Stable Online Algorithm for Energy Efficient Multi User Scheduling", IEEE Transactions on Mobile Computing, vol. 9, no. 10, pp. 1391-1406, Oct. 2010.
- V. S. Borkar, M. K. Ghosh, G. Rangarajan, "Application of nonlinear filtering to credit risk ", Operations Research Letters Volume 38, pp. 527-532, 2010.
- V. S. Borkar, K. Suresh Kumar, "Singular perturbations in risk-sensitive stochastic control ", SIAM J. Control Optim., pp. 3675-3697, 2010.
- V. S. Borkar, K. Suresh Kumar, "A new Markov selection procedure for degenerate diffusions", Journal of Theoretical Probability Volume 23, pp. 729-747, 2010.
- V. S. Borkar, K Suresh Kumar, "McKeanVlasov limit in portfolio optimization ", Stochas-tic Analysis and Applications, pp. 884-906, 2010.
- N. Salodkar, A. Karandikar, V. S. Borkar, "A stable online algorithm for energy-efficient multiuser scheduling", IEEE Trans. on Mobile Computing, pp. , 2010.
- Anup Biswas, V. S. Borkar, "On a controlled eigenvalue problem ", Systems and Control Letters Volume 59, pp. 734-735, 2010.
- Anup Biswas, V. S. Borkar, K. Suresh Kumar, "Risk-sensitive control with near- monotone cost", Applied Mathematics and Optimization Volume 62, pp. , 2010.
- Amar Prakash Azad, Sara Alouf, Eitan Altman, Vivek Borkar, Georgios S. Paschos, "Optimal control of sleep periods for wireless terminals ", IEEE Journal of Selected Areas in Communications, pp. , 2010.
- A. Arapostathis, V. S. Borkar, "Uniform recurrence properties of controlled diffusions and applications to optimal control", SIAM J. Control Optim. Volume 48 Issue 7, pp. , 2010.
- V. S. Borkar, "Cooperative dynamics and Wardrop equilibria", Systems and Control Letters, pp. 91-93, 2009.
- V. S. Borkar, V. Ejov, J. Filar, "On the hamiltonicity gap and doubly stochastic matrices", Random Structures and Algorithms, pp. 502-519, 2009.
- V. S. Borkar, J. Pinto, T. Prabhu, "A new learning algorithm for optimal stopping", Discrete Event Dynamical Systems 19 1, pp. 91-113, 2009.
- V. S. Borkar, D. J. Das, "A novel ACO scheme for emergent optimization via rein-forcement and initial bias", Swarm Intelligence 3 1, pp. , 2009.
- A. Kulkarni, V. S. Borkar, "Finite dimensional approximation and Newton-based algo-rithm for stochastic approximation in Hilbert space", Automatica, pp. 2815-2822., 2009.
- A. Biswas, V. S. Borkar, "Small noise limits for invariant densities for a class of diffusions: a control theoretic view", J. Math. Analysis and Appl., pp. 476-484., 2009.
- Mukul Agarwal, Vivek S Borkar, Abhay Karandikar, "Structural Properties of Optimal Transmission Policies Over a Randomly Varying Channels", IEEE Transactions on Automatic Control, vol. 53, no. 6, pp. 1476-1491, Jul. 2008.
- Nitin Salodkar, Abhijeet Bhorkar, Abhay Karandikar, Vivek Borkar, "An Online Algorithm for Energy Efficient Delay Constrained Scheduling over Fading Channel", IEEE Journal on Selected Areas in Communications, vol. 26, no. 4, pp. 732-742, May 2008.
- V. S. Borkar, D. Manjunath, "Distributed topology control of wireless networks", Wire-less Networks 15, pp. 1022-1038, 2008.
- N. Salodkar, A. Bhorkar, A. Karandikar, V. S. Borkar, "An on-line learning algorithm for energy efficient delay constrained scheduling over a fading channel", IEEE Journal on Selected Areas in Communications 26 4, pp. 732 - 742, 2008.
- M. Agarwal, V. S. Borkar, A. Karandikar, "Structural properties of optimal trans- mission policies over a randomly varying channel", IEEE Transactions on Automatic Control, pp. 1476 - 1491, 2008.
- K. Barman, V. S. Borkar, "A note on linear function approximation using random projections", Systems and Control Letters, pp. 784-786, 2008.
- A. Basu, V. S. Borkar, "Stochastic control with imperfect models", SIAM J. Control and Optim., pp. 1274-1300, 2008.
- A. Basu, T. Bhattacharya, V. S. Borkar, "A learning algorithm for risk-sensitive cost", Mathematics of Operations Research, pp. 880-898, 2008.
- V. S. Borkar, V. Gaitsgory, "Singular perturbations in ergodic control of diffusions", SIAM J. Control and Optimization 46, pp. 1562-1577, 2007.
- V. S. Borkar, V. Gaitsgory, "On averaging of singularly perturbed stochastic differen- tial equations", Applied Maths. and Optimization 56, pp. 169-209, 2007.
- V. Anantharam, V. S. Borkar, "Common randomness and distributed control: a counterexample", Systems and Control Letters 56, pp. 568-572, 2007.
- V. S. Borkar, "Stochastic approximation withcontrolled Markov noise", Systems and Control Letters 55, pp. 139-145, 2006.
- S. Bhatnagar, V. S. Borkar, A. Madhukar, "A simulation-based algorithm for ergodic control of Markov chains conditioned on rare events", J. Machine Learning Research 7, pp. 1937-1962, 2006.
- I. Ahamed, V. S. Borkar, S. Juneja, "Adaptive importance sampling for Markov chains using stochastic approximation", Operations Research 54, pp. 489-504, 2006.
- A. Karnik, A. Kumar, V. S. Borkar, "Distributed self-tuning of sensor networks", Wireless Networks 12, pp. 531-545, 2006.
- V. S. Borkar, "Controlled diffusion processes", Probability Surveys 2, pp. 213-245, 2005.
- V. S. Borkar, "An actor-critic algorithm for constrained Markov decision processes", Systems and Control Letters 54, pp. 207-213, 2005.
- V. S. Borkar, M. Dave, R. K. Shyamasundar, "Design and implementation of SeTiA: secure multi auction system II: implementation issues", Journal of Intelligent Systems, pp. 69-93, 2005.
- V. S. Borkar, M. Dave, R. K. Shyamasundar, "Design and implementation of SeTiA: secure multi auction system I: auction mechanisms", Journal of Intelligent Systems 14, pp. 45-68, 2005.
- G. Rajadhyaksha, V. S. Borkar, "Transmission rate control over randomly varying channels", Probability in Engg. and Info. Sciences 19, pp. 73-82, 2005.
- V. S. Borkar, V. R. Konda, S. K. Mitter, "On De Finetti coherence and Kolmogorov probability", Statistics and Probability Letters and Simulation 79, pp. 417–421, 2004.
- V. S. Borkar, V. Ejov, J. A. Filar, "Directed graphs Hamiltonicity and doubly stochas-tic matrices", Random Structures and Algorithms 25, pp. 376-395, 2004.
- V. S. Borkar, S. R. Venkatesh, S. K. Mitter, "Variations on a theme by Neyman and Pearson Sankhya Part 2", 66, pp. 292-305, 2004.
- V. S. Borkar, S. Juneja, A. A. Kherani, "Performance analysis conditioned on rare events: an adaptive simulation scheme", Communications in Information and Systems, pp. 259-278, 2004.
- V. S. Borkar, D. Manjunath, "Charge-based control of Diffserve-like queues", Auto-matica 40, pp. 2040-2057, 2004.
- V. S. Borkar, A. Budhiraja, "Ergodic control for constrained diffusions: characterization using HJB equations", SIAM J. Control and Optim. 43, pp. 1463-1492, 2004.
- V. S. Borkar, A. Budhiraja, "A further remark on dynamic programming for partially observed Markov processes", Stochastic Processes and Their Appl. 112, pp. 79-93, 2004.
- V. S. Borkar, "Dynamic programmimg for ergodic control with partial observations", Stochastic Processes and Their Applications 103, pp. 293-310, 2003.
- V. S. Borkar, "Avoidance of traps in stochastic approximation", Systems and Control Letters 50, pp. , 2003.
- V. S. Borkar, S. Bhatnagar, "Multiscale chaotic SPSA and smoothed functional algo- rithms for simulation optimization", Simulation: Trans. of the Intl. Soc. for Modelling, pp. 568-580, 2003.
- V. S. Borkar, P. R. Kumar, "Dynamic Cesaro-Wardrop equilibration in networks", IEEE Trans. on Automatic Control 48 3, pp. 382-396, 2003.
- V. S. Borkar, M. K. Ghosh, "Ergodic control of partially degenerate diffusions in a compact domain", Stochastics and Stochastic Reports 75 4, pp. 221-231, 2003.
- V. S. Borkar, "Reinforcement learning in Markovian evolutionary games", Advances in Complex Systems 5, pp. 55-72, 2002.
- V. S. Borkar, "Q-learning for risk-sensitive control", Math. Op. Research. 27, pp. 294-311, 2002.
- V. S. Borkar, "On the lock-in probability of stochastic approximation", Combinatorics Probability and Computing 11, pp. , 2002.
- V. S. Borkar, V. Chandru, S. K. Mitter, "Mathematical programming embeddings of logic", J. Automated Reasoning 29, pp. 91-106, 2002.
- V. S. Borkar, S. P. Meyn, "Risk sensitive control for Markov decision processes with monotone cost", Math. Op. Research. 27, pp. 192-209, 2002.
- J. Abounady, D. Bertsekas, V. S. Borkar, "Stochastic approximation for nonexpansive maps: application to Q-learning", SIAM J. Control and Optim. 41, pp. , 2002.
- V. S. Borkar, "A sensitivity formula for risk-sensitive control and the actor-critic algorithm", Systems and Control Letters 44, pp. 339-346, 2001.
- V. S. Borkar, S. K. Mitter, S. Tatikonda, "Optimal sequential vector quantization of Markov sources", SIAM J. Control and Optim. 40, pp. 135-148, 2001.
- V. S. Borkar, S. K. Mitter, S. Tatikonda, "Markov control problems with communica-tion constraints", Communications in Information and Systems 1, pp. 15-32, 2001.
- J. Abounady, D. Bertsekas, V. S. Borkar, "Learning algorithms for Markov decision processes with average cost", SIAM J. Control and Optim. 40, pp. 681-698, 2001.
- V. S. Borkar, "The value function in ergodic control of diffusion processes with partial observations II", Applicationes Mathematicae 27, pp. 455-465, 2000.
- V. S. Borkar, "Stability of annealing schemes and related processes", Systems and Control Letters 41, pp. 325-331, 2000.
- V. S. Borkar, "Sample complexity for Markov chain self-tuner", Systems and Control Letters 41, pp. 95-105, 2000.
- V. S. Borkar, "Average cost dynamic programming equations for controlled Markov chains with partial observations", SIAM J. Control and Optim. 39, pp. 673-681, 2000.
- V. S. Borkar, "A learning algorithm for discrete time stochastic control", Probability in Engg. and Info. Sciences. 14, pp. 243-248, 2000.
- V. S. Borkar, V. R. Konda, "Actor-critic type learning algorithms for Markov decision processes", SIAM J. Control and Opt. 38, pp. 94-123, 2000.
- V. S. Borkar, S. P. Meyn, "The O.D.E. method for convergence of stochastic approx-imation and reinforcement learning", SIAM J. of Control and Optim. 38, pp. 447-469, 2000.
- V. S. Borkar, "The value function in ergodic control of diffusion processes with partial observations", Stochastics 67, pp. 255-266, 1999.
- V. S. Borkar, S. K. Mitter, "A strong approximation theorem for stochastic recursive algorithms", J. Optimization Theory and Appl. 100, pp. 499-513, 1999.
- V. S. Borkar, S. Jain, G. Rangarajan, "Evolutionary games with multiple time scales", Physica D 125, pp. 155-166, 1999.
- V. S. Borkar, P. Gupta, "Randomized neural networks for learning stochastic depen-dences", IEEE Trans. on Systems Man and Cybernetics 29, pp. 469-480, 1999.
- V. S. Borkar, M. K. Ghosh, P. Sahay, "Optimal control of a stochastic hybrid system with discounted cost", J. Optimization Theory and Appl. 101, pp. 557-580, 1999.
- K. Soumyanath, V. S. Borkar, "An analog scheme for fixed point computation Part 2 - Applications", IEEE Trans. on Circuits and Systems 1: Fundamental Theory and Appl. 46, pp. 442-451 , 1999.
- B. Bharath, V. S. Borkar, "Stochastic approximation algorithms: overview and recent trends", Sadhana Indian Academy of Sciences Proc. in Engg. Sciences 24, pp. 425-452, 1999.
- V. S. Borkar, "Convexity in stochastic control", Differential Equations and Dynamical Systems 6 1/2, pp. 37-49, 1998.
- V. S. Borkar, "Asynchronous stochastic approximation", SIAM J. Control and Optim. 36, pp. 840-851, 1998.
- V. S. Borkar, S. Mundra, "Bayesian parameter estimation and adaptive control of Markov processes with time-averaged cost", Applicationes Mathematicae 25, pp. 339-358, 1998.
- V. S. Borkar, S. Jain, G. Rangarajan, "Generalized replicator dynamics as a model of specialization and diversity in societies", Advances in Complex Systems 1, pp. 325-359, 1998.
- V. S. Borkar, G. Rangarajan, S. Jain, "Dynamics of individual specialization and global diversification in communities", Complexity 3, pp. 50-56, 1998.
- Uma S. Ranjan, V. S. Borkar, P. S. Sastry, "Edge detection through a time-homogeneous Markov system", Journal of IISc 78, pp. 31-43, 1998.
- S. Bhatnagar, V. S. Borkar, "A two time-scale stochastic approximation scheme for simulation-based parametric optimization", Probability in Engineering and Inormational Sciences 12 , pp. 519-531, 1998.
- M. Branicky, V. S. Borkar, S. K. Mitter, "A unified framework for hybrid control: Model and optimal control theory", IEEE Trans. on Automatic Control 43, pp. 31-45, 1998.
- B. Bharath, V. S. Borkar, "Robust parameter optimization of hidden Markov models", Journal of Indian Inst. of Science 78, pp. 119-130, 1998.
- V. S. Borkar, "Stochastic approximations with two time scales", Systems and Control Letters 29, pp. 291-295, 1997.
- V. S. Borkar, V. R. Konda, "The actor-critic algorithm as multi-time-scale stochastic approximation", Sadhana: Proc. of Indian Academy of Sciences Engg. Sciences, pp. 525-543, 1997.
- V. S. Borkar, K. Soumyanath, "An analog scheme for fixed point computation Part 1 - Theory", IEEE Trans. on Circuits and Systems 1: Fundamental Theory and Appl., pp. 351-355, 1997.
- S. Bhatnagar, V. S. Borkar, "Multiscale stochastic approximation for parametric op-timization of hidden Markov models", Probability in Engineering and Informational Sciences 11, pp. 509-522, 1997.
- P. Gupta, V. S. Borkar, "Learning decentralized goal-based vector-quantization", Com-plex Systems 11, pp. 73-106, 1997.
- A. Basak, V. S. Borkar, M. K. Ghosh, "Ergodic control of degenerate diffusions", Stoch. Analysis and Appl. 15, pp. , 1997.
- V. S. Borkar, "Recursive self-tuning control of finite Markov chains", Applicationes Mathematicae, pp. 169-188, 1996.
- V. S. Borkar, "Distributed computation of fixed points of ?-nonexpansive maps", Proc. of Indian Academy of Sciences Math. Sciences, pp. 289-300, 1996.
- V. S. Borkar, S. K. Mitter, "Stochastic processes that generate polygonal and related random fields", IEEE Trans. Info. Theory 42, pp. 606-617, 1996.
- A. Bhatt, V. S. Borkar, "Occupation measures for controlled Markov processes: char-acterization and optimality", Annals of Probability 24, pp. 1531-1562, 1996.
- V. S. Borkar, "A note on ergodic control of degenerate diffusions", J. Opt. Theory and Appl. 86, pp. 251-261, 1995.
- V. S. Borkar, S. Kumar, "On extremal solutions of controlled non-linear filtering equations", SIAM J. Control and Optim. 33, pp. 718-725, 1995.
- V. S. Borkar, M. K. Ghosh, "Recent trends in Markov decision processes", Journal of Indian Inst. of Science, pp. 45778, 1995.
- S. Bhatnagar, V. S. Borkar, "A convex analytic framework for ergodic control of semi-markov processes", Math. Op. Research, pp. 923-936, 1995.
- V. S. Borkar, "Ergodic control of Markov chains with constraints - the general case", SIAM J. Control and Optim. 32, pp. 176-186, 1994.
- V. S. Borkar, V. Phansalkar, "Managing interprocessor delays in distributed recursive algorithms", Sadhana: Indian Academy of Sciences Proc. in Engg. Sciences 19 6, pp. 995-1003, 1994.
- V. S. Borkar, T. E. Govindan, "Optimal control of semilinear stochastic evolution equations in Nonlinear Analysis", : Theory Methods and Applications 23, pp. , 1994.
- V. S. Borkar, "On white noise representations in stochastic realization theory", SIAM J. Control and Optim. 31, pp. 1093-1102, 1993.
- V. S. Borkar, "On the Milito-Cruz adaptive control scheme for Markov chains", J. Optim. Theory and Appl. 77, pp. 385-393, 1993.
- V. S. Borkar, "On infinitesimal ?-fields generated by random processes", Proc. of the Indian Academy of Sciences Math. Sciences, pp. 329-332, 1993.
- V. S. Borkar, "On extremal solutions to stochastic control problems II", Applied Maths.and Optim. 28, pp. 49-56, 1993.
- V. S. Borkar, "Controlled diffusions with constraints II", J. Math. Analysis and Appl. 176, pp. 310-321, 1993.
- V. S. Borkar, M. K. Ghosh, "Denumerable state stochastic games with limiting average payoff", J. Optim. Theory and Appl. 76, pp. 539-560, 1993.
- A. Araposthasis, V. S. Borkar, E. Fernandez-Gaucherand, M. K. Ghosh, S. I. Marcus, "Discrete time controlled Markov processes with average cost criterion – a survey", SIAM J. Control and Optim. 31, pp. 282-345, 1993.
- V. S. Borkar, "Pathwise recurrence orders and simulated annealing", J. Appl. Prob.29, pp. 472-476, 1992.
- V. S. Borkar, M. K. Ghosh, "Stochastic differential games: an occupation measure based approach", J. Optim. Theory and Appl. 73, pp. 359-385, 1992.
- V. S. Borkar, "Self-tuning control of diffusions without the identifiability condition", J. Opt. Theory and Appl., pp. 117-138, 1991.
- V. S. Borkar, "On extremal solutions to stochastic control problems", Applied Maths. and Opt. 24, pp. 317-330, 1991.
- V. S. Borkar, "A remark on control of partially observed Markov chains", Annals of Op. Research 29, pp. 429-438, 1991.
- V. S. Borkar, M. K. Ghosh, "Ergodic and adaptive control of nearest-neighbour motions", Maths. of Control Signals and Systems 4, pp. 81-98, 1991.
- V. S. Borkar, "The Kumar-Becker-Lin scheme revisited", J. Opt. Theory and Appl. 66, pp. 289-309, 1990.
- V. S. Borkar, "Controlled Markov chains with constraints II", Sadhana 15, pp. 405-413, 1990.
- V. S. Borkar, M. K. Ghosh, "Ergodic control of multidimensional diffusions II: adaptive control", Applied Math. and Opt. 21, pp. 191-220, 1990.
- V. S. Borkar, M. K. Ghosh, "Controlled diffusions with constraints", J. Math. Anal. and Appl. 152, pp. 88-108, 1990.
- V. S. Borkar, "Minimum toll control of diffusions", Systems and Control Letters 12, pp. 343-349, 1989.
- V. S. Borkar, "Mimicking finite dimensional marginals of a controlled diffusion by simpler controls", Stoch. Proc. and Their Appl. 31, pp. 333- 342, 1989.
- V. S. Borkar, "Control of Markov chains with long-run average cost criterion: The dynamic programming equation", SIAM J. Control and Opt. 27, pp. 642-657, 1989.
- V. S. Borkar, "A topology for Markov controls", Appl. Math. and Opt. 20, pp. 55-62, 1989.
- V. S. Borkar, "The probabilistic structure of controlled diffusion processes", Acta Appl. Math. 11, pp. 19-48, 1988.
- V. S. Borkar, "Controlled diffusions with boundary crossing costs", Applied Maths. and Opt. 18, pp. 67-83, 1988.
- V. S. Borkar, "A convex analytic approach to Markov decision processes", Prob. The-ory and Related Fields 78, pp. 583-602, 1988.
- V. S. Borkar, R. T. Chari, S. K. Mitter, "Stochastic quantization of field theory in finite and infinite volume", J. Funct. Analysis 81, pp. 184-206, 1988.
- V. S. Borkar, M. K. Ghosh, "Ergodic control of multidimensional diffusions I: the existence results", SIAM J. Control and Opt. 26, pp. 112- 126, 1988.
- V. S. Borkar, "Control of a partially observed diffusions up to an exit time", Systems & Control Letters 8, pp. 429-435, 1987.
- V. S. Borkar, "A comparison principle for certain convex functionals of diffusion process without drift", Stoch. Proc. and Their Appl. 25, pp. 245-248, 1987.
- V. S. Borkar, "The Nisio semigroup for controlled diffusions with partial observations", Stochastics, pp. 145-160, 1986.
- V. S. Borkar, "A remark on the attainable distributions of controlled diffusions", Stochastics 18 1, pp. 17-23, 1986.
- V. S. Borkar, "A note on controlled diffusions with time-averaged cost", Systems & Control Letters, pp. , 1984.
- A. Bensoussan, V. S. Borkar, "Ergodic control problem for one-dimensional diffu-sions with near-monotone cost", Systems & Control Letters, pp. 127-133, 1984.
- V. S. Borkar, "On minimum cost per unit time control of Markov chains", SIAM Journal of Control and Optimization 22 6, pp. 965-978, 1984.
- V. S. Borkar, "Evolution of interacting particles in a Brownian medium", Stochastics 14 1, pp. 33-79, 1984.
- A. Bagchi, V. S. Borkar, "Parameter identification in infinite dimensional linear sys-tems", Stochastics 12 3+4, pp. 201-213, 1984.
- V. S. Borkar, "Existence of optimal controls for partially observed diffusions", Stochastics, pp. 103-141, 1983.
- V. S. Borkar, "Controlled Markov chains and stochastic networks", SIAM Journal of Control and Optimization, pp. 652-666, 1983.
- V. S. Borkar, P. Varaiya, "Asymptotic agreement in distributed estimation", IEEE Transactions on Automatic Control, pp. 650-655, 1982.
- V. S. Borkar, "Pathwise smoothing of Markov processes with noisy observations", J.of Mathematical Analysis and Applications 90 2, pp. 525-535, 1982.
- V. S. Borkar, "Parameter estimation in stochastic systems: some recent results and applications", Systems & Control Letters, pp. 221-226, 1982.
- V. S. Borkar, P. Varaiya, "Identification and adaptive control of Markov chains", SIAM Journal of Control and Optimization, pp. 470-489, 1982.
- V. S. Borkar, A. Bagchi, "Parameter estimation in continuous-time stochastic pro-cesses", Stochastics 8 3, pp. 193-212, 1982.
- V. S. Borkar, P. Varaiya, "Finite chain approximations to continuous stochastic control problems", IEEE Transactions on Automatic Control, pp. 466-470, 1981.
- V. S. Borkar, P. Varaiya, "Adaptive control of Markov chains I: Finite parameter set", IEEE Transactions on Automatic Control, pp. 953-957, 1979.

Books

- V. S. Borkar, A. Arapostathis and M. K. Ghosh, "Ergodic Control of Diffusion Processes ", Cambridge Uni. Press, Cambridge, UK, 2012.
- V. S. Borkar, V. Ejov, J. A. Filar and G. Nguyen, "Hamiltonian cycle problem and Markov chains", Springer Verlag, New York, 2012.
- V. S. Borkar, "Stochastic Approximation: A Dynamical Systems Viewpoint", Hindustan Publ. Agency, New Delhi, and Cambridge Uni. Press, 2008.
- V. S. Borkar, "Probability Theory: An Advanced Course", Springer Verlag, New York, 1995.
- V. S. Borkar (Review by W. Fleming in SIAM Review, Sept. 1990)., "Optimal Control of Diusion Processes", Longman Scientic and Technical, Harlow, England, 1989.

Conference Papers / Book Chapters

- Anh Truong, N. Kiyavash, V. S. Borkar , "Convergence analysis for an online recommendation system" in Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), pp.3889 – 3894, Dec. 2012.
- V. S. Borkar, A. Karnik , "Controlled gossip" in Proc. of the 49th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, pp.707 - 711, Dec. 2011.
- V.S Borkar, R. Sundaresan, "Asymptotics of the invariant measure in mean _eld models with jumps" in Proc. of the 49th Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, pp.1258 - 1263, Dec. 2011.
- V. S. Borkar, J. Kuri , "Optimal distributed uplink channel allocation: a constrained MDP formulation" in Advances in Dynamic Games, Birkhauser, New York, pp.425-445, Dec. 2010.
- V. S. Borkar, "Reinforcement learning - a bridge between numerical methods and Markov chain Monte Carlo" in Perspectives in Mathematical Sciences, World Scientic, Singapore, pp.71-91, Dec. 2009.
- V. S. Borkar, "Reinforcement learning for Markov decision processes" in Advances in Computational Optimization and its Applications, Universities Press, Hyderabad, pp.31-36, Dec. 2007.
- Abhijeet Bhorkar, Abhay Karandikar, Vivek S Borkar, "Power Optimal Opportunistic Scheduling" in IEEE GLOBECOM, Dec. 2006.
- V. S. Borkar , "The `O.D.E.' approach to stochastic approximation" in Mathematical Models for Bioengineering and Probabilistic Systems, Narosa Publ. House, New Delhi, pp.422-445, Dec. 2005.
- E. Altman, V. S. Borkar, A. A. Kherani, P. Michiardi, R. Molva, "Some game theoretic problems in wireless ad-hoc networks" in Mobile and Wireless Systems, Springer Verlag,, pp.82-104., Dec. 2005.
- D. Garg, V. S. Borkar, D. Manjunath, "Network pricing for QoS: a `regulation' approach" in Advances in Control, Communication Networks, and Transportation Systems, Birkhauser, Boston, Dec. 2005.
- V. S. Borkar, S. Jain, G. Rangarajan, "Evolutionary mechanisms of organization in complex systems" in Mathematical Models for Bioengineering and Probabilistic Systems, Narosa Publ. House, pp.323-350, Dec. 2005.
- D. P. Bertsekas, V. S. Borkar, A. Nedic, "Improved temporal dierence methods with linear function approximation" in Handbook of Learning and Approximate Dynamic Programming, Wiley-IEEE Press, Dec. 2004.
- V. S. Borkar, S. K. Mitter, "A note on stochastic dissipativeness" in Directions in Mathematical Systems Theory and Optimization, Berlin - Heidelberg,, pp.41-49, Dec. 2003.
- A. Nedic, D. Bertsekas, V. S. Borkar, "Distributed asynchronous incremental subgradient methods" in Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, Elsevier Scientic Publishers, Dec. 2001.
- Borkar, "Convex analytic methods in Markov decision processes" in Markov Decision Pro- cesses: Models, Methods, Directions and Open Problems, Kluwer Academic,, Dec. 2001.
- "The Proceedings of the Workshop on Recent Advances in Stochastic Models and their Applications " in , Indian Academy of Sciences., Dec. 1991.
- Borkar, "Controlled Markov chains on a countable state space: some recent results" in Recent Advances in Stochastic Calculus, Springer-Verlag, Dec. 1990.
- Borkar, "Control of Markov chains with long-run average cost criterion" in Stochastic Dif- ferential Systems, Stochastic Control Theory and Applications, Springer-Verlag, pp.57-77, Dec. 1988.
- Borkar, "Parameter estimation in stochastic systems'," in Sequential Methods in Statistics, Polish Scientic Publishers, Warsaw., Dec. 1986.