Simple procedure for correcting equations of evolution: Application to Markov processes

Gregory Ryskin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

A general procedure is proposed for correcting evolution equations, arising in different branches of science. Its application to Markov processes shows that the coefficients of the third- and higher-order derivatives in the Kramers-Moyal expansion are, in general, not small; nevertheless, the macroscopic-time evolution of the process is completely described by a differential equation of second order. For Brownian motion, this equation is Galilean invariant, while the Fokker-Planck equation is not. Finally, a correction is derived for the master equation.

Original languageEnglish (US)
Pages (from-to)5123-5127
Number of pages5
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume56
Issue number5
DOIs
StatePublished - Jan 1 1997

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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