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A Stochastic Interpretation of the Cauchy Problem Solution for the Equation ∂u/∂t=(σ^2/2)Δu+V(x)u with Complex σ. / Faddeev, M.M.; Ibragimov, I.A.; Smorodina, N.V.

In: Markov Processes and Related Fields, Vol. 22, No. 2, 2016, p. 203-226.

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@article{b5f3a670488a4aa5926e597ad819acd4,
title = "A Stochastic Interpretation of the Cauchy Problem Solution for the Equation ∂u/∂t=(σ^2/2)Δu+V(x)u with Complex σ.",
abstract = "Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\{"}odinger equation when $\mathrm{Re}\,\sigma^2=0$.",
keywords = "Limit theorem, Schr\{"}odinger equation, Feynman measure, random walk, evolution equation",
author = "M.M. Faddeev and I.A. Ibragimov and N.V. Smorodina",
year = "2016",
language = "English",
volume = "22",
pages = "203--226",
journal = "Markov Processes and Related Fields",
issn = "1024-2953",
publisher = "Polymat",
number = "2",

}

RIS

TY - JOUR

T1 - A Stochastic Interpretation of the Cauchy Problem Solution for the Equation ∂u/∂t=(σ^2/2)Δu+V(x)u with Complex σ.

AU - Faddeev, M.M.

AU - Ibragimov, I.A.

AU - Smorodina, N.V.

PY - 2016

Y1 - 2016

N2 - Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\mathrm{Re}\,\sigma^2=0$.

AB - Using classical probabilistic methods we construct a probabilistic approximation in $L_2$ of the Cauchy problem solution for an equation $\frac{\partial u}{\partial t}=\frac{\sigma^2}{2}\,\Delta u+V(x)u,$ where $\mathrm{Re}\,V\leqslant 0$ and $\sigma$ is a complex parameter with $\mathrm{Re}\,\sigma^2\geqslant 0$. This equation coincides with the heat equation when $\mathrm{Im}\,\sigma=0$ and with the Schr\"odinger equation when $\mathrm{Re}\,\sigma^2=0$.

KW - Limit theorem

KW - Schr\"odinger equation

KW - Feynman measure

KW - random walk

KW - evolution equation

M3 - Article

VL - 22

SP - 203

EP - 226

JO - Markov Processes and Related Fields

JF - Markov Processes and Related Fields

SN - 1024-2953

IS - 2

ER -

ID: 7587928