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Path Integrals for Stochastic Processes: An Introduction

Horacio S. Wio

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Description:This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.Contents: Stochastic Processes: A Short Tour The Path Integral for a Markov Stochastic Process Generalized Path Expansion Scheme I Space-Time Transformation I Generalized Path Expansion Scheme II Space-Time Transformation II Non-Markov Processes: Colored Noise Case Non-Markov Processes: Non-Gaussian Case Non-Markov Processes: Nonlinear Cases Fractional Diffusion Process Feynman–Kac Formula, the Influence Functional Other Diffusion-Like Problems What was Left Out Readership: Advanced undergraduate and graduate students, researchers interested in stochastic analysis and statistical physics.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Path Integrals for Stochastic Processes: An Introduction. To get started finding Path Integrals for Stochastic Processes: An Introduction, you are right to find our website which has a comprehensive collection of manuals listed.
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ISBN: 9814449059

Description: This book provides an introductory albeit solid presentation of path integration techniques as applied to the field of stochastic processes. The subject began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics. However, the true trigger for the application of these techniques within nonequilibrium statistical mechanics and stochastic processes was the work of Onsager and Machlup in the early 1950's. The last quarter of the 20th century has witnessed a growing interest in this technique and its application in several branches of research, even outside physics (for instance, in economy).The aim of this book is to offer a brief but complete presentation of the path integral approach to stochastic processes. It could be used as an advanced textbook for graduate students and even ambitious undergraduates in physics. It describes how to apply these techniques for both Markov and non-Markov processes. The path expansion (or semiclassical approximation) is discussed and adapted to the stochastic context. Also, some examples of nonlinear transformations and some applications are discussed, as well as examples of rather unusual applications. An extensive bibliography is included. The book is detailed enough to capture the interest of the curious reader, and complete enough to provide a solid background to explore the research literature and start exploiting the learned material in real situations.Contents: Stochastic Processes: A Short Tour The Path Integral for a Markov Stochastic Process Generalized Path Expansion Scheme I Space-Time Transformation I Generalized Path Expansion Scheme II Space-Time Transformation II Non-Markov Processes: Colored Noise Case Non-Markov Processes: Non-Gaussian Case Non-Markov Processes: Nonlinear Cases Fractional Diffusion Process Feynman–Kac Formula, the Influence Functional Other Diffusion-Like Problems What was Left Out Readership: Advanced undergraduate and graduate students, researchers interested in stochastic analysis and statistical physics.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Path Integrals for Stochastic Processes: An Introduction. To get started finding Path Integrals for Stochastic Processes: An Introduction, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Path Integrals for Stochastic Processes: An Introduction

Path Integrals for Stochastic Processes: An Introduction

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