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arXiv · 1812.07595

Conditional probabilities in multiplicative noise processes

Miguel V. Moreno·Daniel G. Barci·Zochil González Arenas
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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.

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Miguel V. Moreno, Daniel G. Barci, Zochil González Arenas. 2019-03-09. Conditional probabilities in multiplicative noise processes. https://doi.org/10.1103/physreve.99.032125

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