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 language | English (US) |
|---|---|
| Pages (from-to) | 5123-5127 |
| Number of pages | 5 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 56 |
| Issue number | 5 |
| DOIs | |
| State | Published - 1997 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics