Quasicontinuum fokker-planck equation

Francis J. Alexander, Philip Rosenau

Research output: Contribution to journalArticlepeer-review


Building on the work we present a regularized Fokker-Planck equation for discrete-state systems with more accurate short-time behavior than its standard, Kramers-Moyal counterpart. This regularization leads to a quasicontinuum Fokker-Planck equation with several key features: it preserves crucial aspects of state-space discreteness ordinarily lost in the standard Kramers-Moyal expansion; it is well posed, and it is more amenable to analytical and numerical tools currently available for continuum systems. In order to expose the basic idea underlying the regularization, it suffices for us to focus on two simple problems-the chemical reaction kinetics of a one-component system and a two-dimensional symmetric random walk on a square lattice. We then describe the path to applying this approach to more complex, discrete-state stochastic systems.

Original languageEnglish
Article number041902
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
StatePublished - 2 Apr 2010


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