Journal of Mathematical Physics

Stochastic dynamical interpolation formula to time-reversible diffusion processes

Tetsuya Misawa

Published Feb 1, 1993• 5 citations

Abstract

A diffusion process of which the diffusion property is preserved under time reversal is called a time-reversible diffusion process. A typical example of such a process is found in Nelson’s stochastic mechanics. Within the extended framework of stochastic integrals proposed by Itô, a sort of the interpolation formula, called a stochastic dynamical interpolation formula, to the time-reversible diffusion process, is derived from a pinned process for the diffusion process. It is shown that the stochastic interpolation formula is regarded as an extention of Lévy’s interpolation formula, which is obtained on the basis of a pinned Brownian motion.

DOI: 10.1063/1.530221

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