Markov Processes: Theorems and Problems

One Contraction semigroups of linear operators on Banach spaces.- Two Infinitesimal operators of transition functions.- Three Markov processes.- Four First entrance and exit times and the intrinsic topology in the state space.- Five Characteristic operators of Markov processes. Differential generators of diffusion processes.- Six Functionals of Markov processes.- Seven Stochastic integrals.- Eight Nonnegative additive functionals of a Wiener process.- Nine Transition functions, corresponding to almost multiplicative functionals.- Ten Transformations of Markov processes.- Eleven Stochastic integral equations and diffusion processes.- Twelve Excessive, superharmonic and harmonic functions.- Thirteen Harmonic and superharmonic functions associated with strong Feller processes. Probabilistic solution of certain equations.- Fourteen The multi-dimensional Wiener process and its transformations.- Fifteen Continuous strong Markov processes on a closed interval.- Sixteen Continuous strong Markov processes on an open interval.- Seventeen Construction of one-dimensional continuous strong Markov processes.- § 1. Measurable spaces and measurable transformations.- § 2. Measures and integrals.- § 3. Probability spaces.- § 4. Martingales.- § 5. Topological measurable spaces.- § 6. Some theorems on partial differential equations.- § 7. Measures and countably additive set functions on the line and corresponding point functions.- § 8. Convex functions.- Historical-bibliographical note.- List of symbols.- List of symbols.