Mathematical Statistics: Stationary Stochastic Processes

<p>An introductory course in stochastic processes.</p><p>The course treats stochastic processes in discrete and continuous time. The main elements are:</p> <p>Models for stochastic dependence.Concepts of description of stationary stochastic processes in the time domain: expectation, covariance, and cross-covariance functions. Concepts of description of stationary stochastic processes in the frequency domain: effect spectrum, cross spectrum. Special processes: Gaussian process, Wiener process, white noise, Gaussian fields in time and space. Stochastic processes in linear filters: relationships between in- and out-signals, auto regression and moving average (AR, MA, ARMA), derivation and integration of stochastic processes. The basics in statistical signal processing: estimation of expectations, covariance function, and spectrum. Application of linear filters: frequency analysis and optimal filters.</p>