Markov Processes

Inhaltsverzeichnis

• 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.