Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription

Zochil González Arenas, Daniel G. Barci, and Constantino Tsallis
Phys. Rev. E 90, 032118 – Published 16 September 2014

Abstract

We deduce a nonlinear and inhomogeneous Fokker-Planck equation within a generalized Stratonovich, or stochastic α, prescription (α=0, 1/2, and 1, respectively, correspond to the Itô, Stratonovich and anti-Itô prescriptions). We obtain its stationary state pst(x) for a class of constitutive relations between drift and diffusion and show that it has a q-exponential form, pst(x)=Nq[1(1q)βV(x)]1/(1q), with an index q which does not depend on α in the presence of any nonvanishing nonlinearity. This is in contrast with the linear case, for which the index q is α dependent.

  • Received 19 June 2014

DOI:https://doi.org/10.1103/PhysRevE.90.032118

©2014 American Physical Society

Authors & Affiliations

Zochil González Arenas1, Daniel G. Barci2, and Constantino Tsallis1

  • 1Centro Brasileiro de Pesquisas Físicas, National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
  • 2Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil

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Vol. 90, Iss. 3 — September 2014

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