Lectures on the Theory of Stochastic Processes

ISBN: 9789067642064 出版年：1996 页码：192 Skorochod, Anatolij V De Gruyter

Stochastic processes - definitions, examples the Kolmogorov consistency theorem - classification of processes random walks - recurrence, renewal theorem Martingales - inequalities for Martingales theorems on the limit of a Martingale stationary sequences - ergodic theorem ergodic theorem - metric transitivity regularization of a process continuity processes without discontinuities of the second kind continuity of processes with independent increments - Martingales with continuous time measurable processes stopping times - associated s-algebras completely measurable processes L2-theory stochastic integrals stationary processes - spectral representations stationary sequences - regularity and singularity the prediction of a stationary sequence Markov processes homogeneous Markov processes and associated semigroups homogeneous purely discontinuous processes - conditions for their regularity processes with de-numerable set of states simple birth and death processes branching processes with particles of only one kind homogeneous processes and strongly continuous semigroups resolvent operator and generator the Hille-Iosida theorem processes with independent increments - representation of the discontinuous part general representation of a stochastically continuous process with independent increments diffusion processes stochastic integrals existence, uniqueness and properties of solutions of stochastic differential equations Ito's formula with some corollaries.