English

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.

Keywords

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

R2 v1 2026-06-23T06:46:52.704Z