Theory and Applications of Stochastic Processes: An Analytical Approach / Edition 1

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Shastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical.

This book offers an analytical approach to shastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

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Editorial Reviews

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“It intends to investigate the role of shastic processes in questions from physics or engineering, to explore the strong relationship between shastic and partial differential equations and to provide analytical approximations to the solutions. … The book will be very helpful to people working in disciplines like statistical physics, physical chemistry, molecular biophysics, and communications theory. … Endowed with numerous exercises and worked-out examples, it may also provide graduate students with a well-thought-out two-semester course on shastic processes and their applications.”­­­ (Dominique Lépingle, Mathematical Reviews, Issue 2011 d)

“This book is something for which many have been long awaiting. It provides a rather in-depth presentation of the analytical approach to shastic processes with continuous paths. … The methods developed in the text are very accessible to applied mathematicians with a basic background in probability theory. This is a timely and unique contribution, from one of its leading researchers over four decades, to an exciting area of applied mathematics with ever-growing importance.” (Hong Qian, SIAM Review, Vol. 53 (1), 2011)

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Product Details

  • ISBN-13: 9781441916044
  • Publisher: Springer New York
  • Publication date: 12/21/2009
  • Series: Applied Mathematical Sciences Series, #170
  • Edition description: 2010
  • Edition number: 1
  • Pages: 468
  • Product dimensions: 6.40 (w) x 9.30 (h) x 1.40 (d)

Table of Contents

Introduction.- The Physical Brownian Motion: Diffusion and Noise.- The Probability Space of Brownian Motion.- Ito Integration and Calculus.- Shastic Differential Equations.- The Discrete Approach and Boundary Behavior.- The First Passage Time of Diffusions.- Markov Processes and Diffusion Approximations.- Diffusion Approximations to Langevin's Equation.- Large Deviations of Markovian Jump Processes.- Noise-Induced Escape from an Attractor.- Shastic Stability.- Bibliography.
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