## A Course in the Theory of Stochastic Processes |

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### Contents

Basic Concepts | 7 |

Elements of Random Analysis | 28 |

General Concepts and Correlation Theory | 42 |

Copyright | |

11 other sections not shown

### Common terms and phrases

apply arbitrary assume Banach space belongs bounded called closed condition connected consider consists contains continuous convergence correlation function corresponding countable course defined definition density derivative determined differentiable diffusion distribution elements equal equation example exists fact family of o-algebras finite finite-dimensional distributions follows formula given Hence increments independent interval limit linear Markov family Markov process Markov property mathematical expectation mean mean square measurable measurable with respect Microtheorem nonnegative o-algebra F obtain operator particular paths Prob probability Problem proof prove random function random process random variable reach remains respect result satisfied segment semigroup sense sequence side singular solution space stationary process step subsets sufficient suppose surely theorem theory tion transition function uniformly uniquely valid values verify Wiener process zero