Conditional probabilities in multiplicative noise processes
Statistical Mechanics
2019-03-27 v2
Abstract
We address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach. We show the equivalence between the conditional probability and the propagator of a quantum particle with variable mass. Introducing a {\em time reparametrization}, we are able to transform the problem of multiplicative noise fluctuations into an equivalent additive one. We illustrate the method by showing the explicit analytic computation of the conditional probability of a harmonic oscillator in a nonlinear multiplicative environment.
Cite
@article{arxiv.1812.07595,
title = {Conditional probabilities in multiplicative noise processes},
author = {Miguel V. Moreno and Daniel G. Barci and Zochil González Arenas},
journal= {arXiv preprint arXiv:1812.07595},
year = {2019}
}
Comments
12 pages, 4 figures. Final version accepted for publication in Physical Review E