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Book
Controlled diffusion processes
Authors: ---
ISBN: 0387904611 3540904611 9783540904618 9780387904610 Year: 1980 Volume: 14 Publisher: New York (N.Y.): Springer,


Book
Gaussian random processes
Authors: --- ---
ISBN: 038790302X 354090302X 1461262771 1461262755 9780387903026 Year: 1978 Volume: 9 Publisher: New York (N.Y.): Springer,

Statistics of random processes.. 1, General theory
Authors: --- ---
ISBN: 3540639292 3540639284 364208365X 3662100282 3642083668 3662130432 9783540639299 Year: 2001 Volume: 5-6 Publisher: Berlin: Springer,

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Abstract

The subject of these two volumes is non-linear filtering (prediction and smoothing) theory and its application to the problem of optimal estimation, control with incomplete data, information theory, and sequential testing of hypothesis. The required mathematical background is presented in the first volume: the theory of martingales, stochastic differential equations, the absolute continuity of probability measures for diffusion and Ito processes, elements of stochastic calculus for counting processes. The book is not only addressed to mathematicians but should also serve the interests of other scientists who apply probabilistic and statistical methods in their work. The theory of martingales presented in the book has an independent interest in connection with problems from financial mathematics. In the second edition, the authors have made numerous corrections, updating every chapter, adding two new subsections devoted to the Kalman filter under wrong initial conditions, as well as a new chapter devoted to asymptotically optimal filtering under diffusion approximation. Moreover, in each chapter a comment is added about the progress of recent years.

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