Author | Dynkin, E. B. author |
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Title | Markov Processes [electronic resource] : Volume 1 / by E. B. Dynkin |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1965 |
Connect to | http://dx.doi.org/10.1007/978-3-662-00031-1 |
Descript | XII, 366 p. 1 illus. online resource |
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 -- ยง 1. Measurable spaces and measurable transformations -- ยง 2. Measures and integrals -- ยง 3. Probability spaces -- ยง 4. Martingales -- ยง 5. Topological measurable spaces -- ยง 6. Some theorems on partial differential equations -- ยง 7. Measures and countably additive set functions on the line and corresponding point functions -- ยง 8. Convex functions -- Historical-bibliographical note -- List of symbols -- List of symbols