Phys. Rev. E 56, 5123–5127 (1997)Simple procedure for correcting equations of evolution: Application to Markov processesReceived 28 May 1996; published in the issue dated November 1997 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. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.56.5123
DOI:
10.1103/PhysRevE.56.5123
PACS:
05.40.+j, 02.50.Ga, 02.20.Mp
|
|
About | Terms and Conditions | Subscriptions | Search | Help
Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. Physical Review®, Physical Review Letters®, Reviews of Modern Physics®, and Physical Review Special Topics® are trademarks of the American Physical Society.