Ito, stratonovich and kinetic forms of stochastic equations

Yu.L. Klimontovich

Physica A: Statistical Mechanics and its Applications, 1990, vol. 163, issue 2, 515-532

Abstract: The well known Ito and Stratonovich forms of presentation of stochastic equations are not, in general, physically equivalent. From the point of view of the statistical theory of nonequilibrium processes the third is most natural-the “kinetic form” of presentation of the Langevin and corresponding Fokker-Planck equations. Only in this case exist fluctuation- dissipation relations (the Einstein formula) for nonlinear systems. For the confirmation of this point of view the following different concrete systems are considered: Brownian motion of particles in a medium with nonlinear friction, of the Van der Pol oscillators and others. The connection between the master equation and the Fokker-Planck one is also considered.

Date: 1990
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:163:y:1990:i:2:p:515-532

DOI: 10.1016/0378-4371(90)90142-F

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