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Essentials of probability theory and mathematical
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according according to Theorem Applying assumed assumption bounded called Chapter condition Consequently consider construction convergence Corollary corresponding deduce defined definition Denote density diffusion type equality equivalent establish estimate example exists expectation expl F,-measurable fact filtering follows function function f Further Gaussian given Hence independent inequality introduce Ito formula Lemma limit linear Markov processes mathematical matrix mean measurable modification natural nonanticipative nonlinear nonnegative Note observable obtain optimal Osts particular permits probability space problems PROOF properties proving random process random variable regular representation respect result right continuous satisfied sequence Shiryayev shown solution solution of Equation square integrable martingale statistics stochastic differential equations stochastic integrals strong solution submartingale sufficient supermartingale taking Theorem theory trajectories uniformly integrable unique values w)ds w)dW Wiener process zero