Review of probability theory and random variables: Transformation (function) of random variables, Conditional expectation;Sequences of random variables: convergence of sequences of random variables.;Stochastic processes: wide sense stationary processes, orthogonal increment processes, Wiener process, and the Poisson process, KL expansion.; Ergodicity, Mean square continuity, mean square derivative and mean square integral of stochastic processes.; Stochastic systems: response of linear dynamic systems (e.g. state space or ARMA systems) to stochastic inputs, Lyapunov equations, correlational function, power spectral density function, introduction to linear least square estimation, Wiener filtering and Kalman filtering.
A. Papoulis, Probability, Random Variables and stochastic processes, 2nd Ed., McGraw Hill, 1983.
A. Larson and B.O. Schubert, Stochastic Processes, Vol.I and II, Holden-Day, 1979.
W. Gardener, Stochastic Processes, McGraw Hill, 1986.