Faculty of Science

Objectives

To introduce the concept of wide sense stationary processes and processes relevant to stochastic analysis but, above all, to the statistics of stochastic processes and statistics.

Contents

Wide sense stationary processes (L2-theory); Spectral representation of the covariance function; Orthogonal stochastic measures and integrals; Estimation of the covariance function and the spectral density; Worlds expansion, extrapolation, interpolation and filtering; Kalman Bucy Filter; Gaussian processes; Infinite divisible distributions and Levy-Chintschin representations of characteristic functions; Processes with independent and stationary increments- Levy processes; Stochastic integrals with respect to processes with independent and stationary increments; introduction to delay, deterministic and stochastic equations.