Green’s-function solution for a special class of master equations

12722 10 56394 2 158363 document 56394 Green’s-function solution for a special class of master equations.pdf application/pdf 921c4d80721c264a6a5026f97ef84d3c MD5 799442 2016-05-20 07:45:54 https://pure.iiasa.ac.at/id/eprint/12722/1/Green%E2%80%99s-function%20solution%20for%20a%20special%20class%20of%20master%20equations.pdf 12722 1 1 application/pdf text en public cc_by

Green’s-function solution for a special class of master equations.pdf

published 56395 2 158366 document 56395 lightbox.jpg image/png 0804f27e229b835ee8f0043ace6be68a MD5 72723 2016-05-20 07:46:23 https://pure.iiasa.ac.at/id/eprint/12722/2/lightbox.jpg 12722 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/56394 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/56394 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/56394 archive 5 disk0/00/01/27/22 2016-04-15 11:33:12 2021-08-27 17:26:38 2016-04-15 11:33:12 article show Eder O.J. Lackner T. Posch M. 6733 0000-0001-8649-9129 Green’s-function solution for a special class of master equations pub prog_aci We consider a one-dimensional stochastic process described by a master equation and calculate the time-dependent distribution function. The time evolution of the system is given by the conditional probability h(x,t‖x0), where x and x0 are continuous variables. Assuming a quite general dependence of the transition probability WΩ(x→x’) on a parameter Ω, we show that the backward form of the master equation can be used to calculate arbitrary conditional averages 〈f(x)‖x0⟩t up to any given power in Ω−1. This general expansion procedure will be used to construct h(x,t‖x0) itself. We show that—introducing a new stochastic variable y—the conditional probability h(x,t‖x0) can be expanded into a series of Hermite functions. The coefficients of this expansion, bn(t), which depend on the expansion parameter Ω, can be uniquely determined via a recursion relation. We show that in the limit Ω→∞ all coefficients bn(t) vanish, except b0, which is time independent. In this limit a Gaussian distribution for the conditional probability is obtained, which is in agreement with the so-called linear noise approximation. 1985 published American Physical Society 10.1103/PhysRevA.31.366 3069 public Physical Review A 31 1 366-377 TRUE 0556-2791 FALSE info:eu-repo/semantics/article