The Probabilistic Approximation of the Dirichlet Initial Boundary Value Problem Solution for the Equation $\partial u/\partial t=(\sigma^2/2)/\Delta u$ With a Complex Parameter $\sigma$

#### M.M. Faddeev, I.A. Ibragimov, N.V. Smorodina

2014, v.20, №3, 391-414

ABSTRACT

In the present paper we consider an initial boundary value problem for the equation $\partial u / \partial t = (\sigma^2/2)\Delta u$ where $\sigma$ is a complex parameter $Re \sigma^2\geq 0$ and construct the probabilistic approximation of the solution.

Keywords: random processes,evolution equation,limit theorem,Feynman measure,initial boundary value problem