Journal of Interdisciplinary Mathematics

Path integral representation for the solution of a stochastic Schrodinger equation driven by a semimartingale

Luis A. Rincón

Published Jan 1, 2004• 5 citations

Abstract

In this paper we prove a path integral representation in configuration space for the solution of a stochastic Schrödinger equation driven by a continuous semimartingale. We follow the approach of path integration established by Itô Albeverio and Høegh-Krohn. The equation we consider is the classical Schrödinger equation plus the stochastic term K(t, x)Ψt(x) o dMt, where Mt is a continuous semimartingale. As an application of our result we solve the equation for a stochastic quantum harmonic oscillator. We solve the path integral representation twice, first by discretising the path integral and also by a change of variable. We finally give the solution to the corresponding stochastic heat equation.

DOI: 10.1080/09720502.2004.10700368

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