Foundations of Stochastic Analysis (Dover Books on Mathematics) - Softcover

Rao, M M

Softcover

ISBN 10: 0486481220 ISBN 13: 9780486481227

Publisher: Dover Publications Inc., 2011

Synopsis

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.

Edition details

• Publisher: Dover Publications Inc.
• Publication date: 2011
• Language: English
• ISBN 10: 0486481220
• ISBN 13: 9780486481227
• Binding: Paperback
• Number of pages: 295