Monte Carlo estimates of the solution of a parabolic equation and its derivatives made by solving stochastic differential equations

In this paper a method of estimation of both the solution to a parabolic boundary value problem and its derivatives with respect to parameters and spatial variables is proposed. The method uses a probability representation of a solution of a parabolic equation in the form of a functional of a diffus...

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Bibliographic Details
Published inCommunications in nonlinear science & numerical simulation Vol. 9; no. 2; pp. 177 - 185
Main Author Gusev, S.A.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.04.2004
Subjects
Euler method
Parabolic equation
Parametric derivative
Stochastic differential equation
35K20
Parabolic equation
65C30
60J60
35B30
65C05
Euler method
Parametric derivative
60H35
Stochastic differential equation
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Summary:In this paper a method of estimation of both the solution to a parabolic boundary value problem and its derivatives with respect to parameters and spatial variables is proposed. The method uses a probability representation of a solution of a parabolic equation in the form of a functional of a diffusion process. This process is the solution of a system of stochastic differential equations (SDE) corresponding to the parabolic operator. To obtain the derivatives of the solution of the parabolic boundary value problem the differentiation of the SDE system with respect to the parameters or the initial data is applied.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1007-5704
1878-7274
DOI:10.1016/S1007-5704(03)00108-4