Faculty of Science

Objectives

To give the student a solid introduction to the general theory of Markov processes. These processes occur as solutions of stochastic differential equations, and besides, they are widely used in stochastic modelling.

Contents

Conditional expectations with respect to -algebras; Markov Process on a general state space (E,T); Equivalent formulations of the Markov property; Regular conditional probabilities and transition functions; Finite dimensional distributions, Chapman Kolmogorov equation; Feller Processes and Operators defined by a markov process; Homogeneous processes, The strong Markov property; The reflection principle for Brownian motion; Stationary Markov Processes; Infinitesimal operators of semi groups; Infinitesimal generator of a Markov process; Diffusions and diffusion processes; Backward and Forward Kolmogorov equations.