I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “On a probabilistic method of solving a one-dimensional initial-boundary value problem”, Teor. Veroyatnost. i Primenen., 2013, Volume 58, Issue 2,Pages <nobr>255

This article is cited in 4 papers

On a probabilistic method of solving a one-dimensional initial-boundary value problem

I. A. Ibragimov^a, N. V. Smorodina^b, M. M. Faddeev^b

^a St. Petersburg Department of V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences
^b St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: We obtain an analogue of probabilistic representation of a solution of an initial-boundary value problem for the equation $\partial u/\partial t+(\sigma^2/2)\partial^2u/\partial x^2+f(x)u=0$, where $\sigma$ is a complex number.

Keywords: random processes; evolution equation; limit theorems; Feynman–Kac formula; Feynman integral; Feynman measure.

MSC: 60

Received: 01.11.2012

DOI: 10.4213/tvp4506