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, M.M. Faddeev

Research output

2 Citations (Scopus)

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 $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\sigma$ is a complex parameter such that $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\sigma^2=iS$ where $S$ is a positive number.
Original languageEnglish
Pages (from-to)4455 --- 4472
JournalStochastic Processes and their Applications
Volume125
Issue number12
DOIs
Publication statusPublished - 2015
Externally publishedYes

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