Lecture Notes for the course Stochastic Processes


CONTENT
01. Random variable and random process. Classes of random processes
(Overview).
02. Convergence with probability one and in probability. Other types of
convergence. Ergodic theorem.
03. Orthogonal projection. Conditional expectation in the wide sense.
04. Wiener filter.
05. Kalman filter.
06. Kalman filter implementation for linear algebraic equations. Karhunen
Loeve decomposition.
07. Independence. The conditional expectation.
08. Non linear filtering.
09. Gaussian random sequences.
10. Wiener process. Gaussian white noise.
11. Poisson process. Poisson white noise. Telegraphic signal.
12. Stochastic Itˆo integral.