Stochastic solution of the linearized Boltzmann equation

Mark A. Pinsky

doi:10.1007/BF01012837

Stochastic solution of the linearized Boltzmann equation

Mark A. Pinsky^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process. The integral is only shown to converge conditionally, where the limiting process is defined by an increasing sequence of stopping times. The notion of local martingale plays an important role. A number of related kinetic models are also mentioned.

Original language	English (US)
Pages (from-to)	189-196
Number of pages	8
Journal	Journal of Statistical Physics
Volume	13
Issue number	3
DOIs	https://doi.org/10.1007/BF01012837
State	Published - Sep 1 1975

Keywords

Linearized Boltzmann equation
jump Markov process
multiplicative functional
path integral representation

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01012837

Cite this

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AB - For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process. The integral is only shown to converge conditionally, where the limiting process is defined by an increasing sequence of stopping times. The notion of local martingale plays an important role. A number of related kinetic models are also mentioned.

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KW - path integral representation

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Stochastic solution of the linearized Boltzmann equation

Abstract

Keywords

ASJC Scopus subject areas

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