Limit theorems for symmetric random walks and probabilistic approximation of the Cauchy problem solution for Schrödinger type evolution equations

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

Stochastic Processes and their Applications, 2015, vol. 125, issue 12, 4455-4472

Abstract: In the present paper we discuss a possibility to construct both a probabilistic representation and a probabilistic approximation of the Cauchy problem solution for an equation ∂u∂t=σ22Δu+V(x)u, where σ is a complex parameter such that Reσ2⩾0. This equation coincides with the heat equation when Imσ2=0 and with the Schrödinger equation when σ2=iS where S is a positive number.

Keywords: Limit theorem; Schrödinger equation; Feynman measure; Random walk (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2015.07.005

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