Non-Markov stochastic processes satisfying equations usually associated with a Markov process |
| |
Authors: | J L McCauley |
| |
Institution: | 1.Physics Department,University of Houston,Houston,Texas,USA |
| |
Abstract: | There are non-Markov Ito processes that satisfy the Fokker-Planck, backward time Kolmogorov, and Chapman-Kolmogorov equations.
These processes are non-Markov in that they may remember an initial condition formed at the start of the ensemble. Some may
even admit 1-point densities that satisfy a nonlinear 1-point diffusion equation. However, these processes are linear, the
Fokker-Planck equation for the conditional density (the 2-point density) is linear. The memory may be in the drift coefficient
(representing a flow), in the diffusion coefficient, or in both. We illustrate the phenomena via exactly solvable examples.
In the last section we show how such memory may appear in cooperative phenomena. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|