Random walk in a quasicontinuum

Journal Article · Wed Jul 15 00:00:00 EDT 1987 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.36.985· OSTI ID:6490163

Doering, C R; Hagan, P S; Rosenau, P

A continuous-time random walk on a spatial lattice described by the Kramers-Moyal expansion has a continuum limit described by a Fokker-Planck equation. It is often desirable to know corrections to quantities computed in the continuum limit, but truncation of the Kramers-Moyal expansion at any level other than the Fokker-Planck either breaks down or yields unphysical results. Here we introduce an alternative approximation to the Kramers-Moyal expansion which circumvents the problems of a naive truncation and correctly incorporates the first-order corrections due to the discrete lattice.

• Research Organization: Center for Nonlinear Studies and Theoretical Division, MS-B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
• OSTI ID: 6490163
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 36:2; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRECTIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FOKKER-PLANCK EQUATION
MARKOV PROCESS
PARTIAL DIFFERENTIAL EQUATIONS
SERIES EXPANSION
STOCHASTIC PROCESSES