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Classical Probability Theory and Stochastic Processes

Heinz-Peter Breuer and Francesco Petruccione

in The Theory of Open Quantum Systems

Published in print:
2007
Published Online:
January 2010
ISBN:
9780199213900
eISBN:
9780191706349
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199213900.003.01
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter contains a survey of classical probability theory and stochastic processes. It starts with a description of the fundamental concepts of probability space and Kolmogorov axioms. These ... More


Properties of Langevin and Fokker–Planck equations

Helmut Hofmann

in The Physics of Warm Nuclei: with Analogies to Mesoscopic Systems

Published in print:
2008
Published Online:
September 2008
ISBN:
9780198504016
eISBN:
9780191708480
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504016.003.0025
Subject:
Physics, Nuclear and Plasma Physics

This chapter introduces Langevin- and Fokker-Planck equations by way of a heuristic approach to the physics of Brownian particles. Variances of physical quantities are defined and related to ... More


Continuous Markov process theory

Daniel T. Gillespie and Effrosyni Seitaridou

in Simple Brownian Diffusion: An Introduction to the Standard Theoretical Models

Published in print:
2012
Published Online:
January 2013
ISBN:
9780199664504
eISBN:
9780191748516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199664504.003.0007
Subject:
Physics, Soft Matter / Biological Physics

Three years after Einstein published his groundbreaking 1905 paper on diffusion, a different analysis was published by Paul Langevin. Although it was not clearly appreciated at the time, Langevin's ... More


STOCHASTIC PROCESSES

Robert M. Mazo

in Brownian Motion: Fluctuations, Dynamics, and Applications

Published in print:
2008
Published Online:
January 2010
ISBN:
9780199556441
eISBN:
9780191705625
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199556441.003.0003
Subject:
Physics, Condensed Matter Physics / Materials

This chapter extends the ideas of Chapter 2 by introducing the notion of stochastic process or random process and its distribution functions. The idea of a Markov process is defined. The ... More


Generalized diffusion processes and the Fokker‐Planck equation

Peter Richmond, Jürgen Mimkes, and Stefan Hutzler

in Econophysics and Physical Economics

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199674701
eISBN:
9780191780066
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199674701.003.0007
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the Chapman-Kolmogorov equation, but limits the scope to Markov processes. It is shown here how it can be reduced to the Fokker-Planck partial differential equation, using the ... More


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