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Elements of Random Analysis
General Concepts and Correlation Theory
11 other sections not shown
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