Path Integrals and Perturbation Theory for Stochastic Processes

Ronald Dickman; Ronaldo Vidigal

doi:10.1590/s0103-97332003000100005

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arXiv · cond-mat/0205321

Path Integrals and Perturbation Theory for Stochastic Processes

Ronald Dickman·Ronaldo Vidigal

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Abstract

We review and extend the formalism introduced by Peliti, that maps a Markov process to a path-integral representation. After developing the mapping, we apply it to some illustrative examples: the simple decay process, the birth-and-death process, and the Malthus-Verhulst process. In the first two cases we show how to obtain the exact probability generating function using the path integral. We show how to implement a diagrammatic perturbation theory for processes that do not admit an exact solution. Analysis of a set of coupled Malthus-Verhulst processes on a lattice leads, in the continuum limit, to a field theory for directed percolation and allied models.

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BibTeX RIS

Ronald Dickman, Ronaldo Vidigal. 2002-05-15. Path Integrals and Perturbation Theory for Stochastic Processes. https://doi.org/10.1590/s0103-97332003000100005

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