title: Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription.
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 p(st)(x) for a class of constitutive relations between drift and diffusion and show that it has a q-exponential form, p(st)(x)=N(q)[1-(1-q)βV(x)](1/(1-q)), 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.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil.
authors.forename: Zochil González
authors.initials: ZG
authors.lastname: Arenas
authors.affiliation: Departamento de Física Teórica, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil.
authors.forename: Daniel G
authors.initials: DG
authors.lastname: Barci
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil.
authors.forename: Constantino
authors.initials: C
authors.lastname: Tsallis
mesh_terms: D004058:Diffusion; D008390:Markov Chains; D017711:Nonlinear Dynamics