Foundations of Stochastic Analysis

Nonfiction, Science & Nature, Mathematics, Statistics
Cover of the book Foundations of Stochastic Analysis by M. M. Rao, Dover Publications
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Author: M. M. Rao ISBN: 9780486296531
Publisher: Dover Publications Publication: April 17, 2013
Imprint: Dover Publications Language: English
Author: M. M. Rao
ISBN: 9780486296531
Publisher: Dover Publications
Publication: April 17, 2013
Imprint: Dover Publications
Language: English

Stochastic analysis involves the study of a process involving a randomly determined sequence of observations, each of which represents a sample of one element of probability distribution. This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods.
Starting with the introduction of the basic Kolmogorov-Bochner existence theorem, the text explores conditional expectations and probabilities as well as projective and direct limits. Subsequent chapters examine several aspects of discrete martingale theory, including applications to ergodic theory, likelihood ratios, and the Gaussian dichotomy theorem. Prerequisites include a standard measure theory course. No prior knowledge of probability is assumed; therefore, most of the results are proved in detail. Each chapter concludes with a problem section that features many hints and facts, including the most important results in information theory.

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Stochastic analysis involves the study of a process involving a randomly determined sequence of observations, each of which represents a sample of one element of probability distribution. This volume considers fundamental theories and contrasts the natural interplay between real and abstract methods.
Starting with the introduction of the basic Kolmogorov-Bochner existence theorem, the text explores conditional expectations and probabilities as well as projective and direct limits. Subsequent chapters examine several aspects of discrete martingale theory, including applications to ergodic theory, likelihood ratios, and the Gaussian dichotomy theorem. Prerequisites include a standard measure theory course. No prior knowledge of probability is assumed; therefore, most of the results are proved in detail. Each chapter concludes with a problem section that features many hints and facts, including the most important results in information theory.

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