On time reversibility in stochastic differential equations

Resumo

Stochastic differential equations and its applications are a subject of great interest for scientific research. In this area, Langevin and Fokker-Planck formalisms are extensively used. Systems modeled by differential stochastic equations with additive noise have been largely studied and are the most popular models. However, the understanding of the stochastic dynamics and the evolution to equilibrium for systems dealing with multiplicative noise is difficult and there is a lack of general tools for its characterization. In particular, for the multiplicative noise case, the Fokker-Planck equation does depend on the chosen prescription for the stochastic integration of the associated Langevin equation.[...]