On an Approximation for the Solutions of Some Evolution Equations by the Expectations of Random Walks Functionals

Abstract

The paper deals with some problems concerning probabilistic representation and probabilistic approximation for solution of the Cauchy problem for the family of equations \( \frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\varDelta u \) with complex parameter σ such that Reσ² ≥ 0. This family coincides with the heat equation if Imσ = 0, and with the Schrӧdinger equation if Reσ² = 0. Bibliography: 5 titles