An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula

This paper introduces an asymptotic expansion for the smooth solution of a semi-linear partial differential equation. Our scheme is based on Itô’s formula, Taylor’s expansion, nonlinear Feynman–Kac formula and some algebras.

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Main Author: Kaori Okuma
Format: Article
Language:English
Published: World Scientific Publishing 2024-12-01
Series:International Journal of Mathematics for Industry
Subjects:
Online Access:https://www.worldscientific.com/doi/10.1142/S2661335224500023
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author Kaori Okuma
author_facet Kaori Okuma
author_sort Kaori Okuma
collection DOAJ
description This paper introduces an asymptotic expansion for the smooth solution of a semi-linear partial differential equation. Our scheme is based on Itô’s formula, Taylor’s expansion, nonlinear Feynman–Kac formula and some algebras.
format Article
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institution Kabale University
issn 2661-3352
2661-3344
language English
publishDate 2024-12-01
publisher World Scientific Publishing
record_format Article
series International Journal of Mathematics for Industry
spelling doaj-art-74073fc62ed347e1a49e75b461316a312025-01-31T06:15:28ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500023An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formulaKaori Okuma0Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, JapanThis paper introduces an asymptotic expansion for the smooth solution of a semi-linear partial differential equation. Our scheme is based on Itô’s formula, Taylor’s expansion, nonlinear Feynman–Kac formula and some algebras.https://www.worldscientific.com/doi/10.1142/S2661335224500023Itô’s formulaTaylor’s expansionnonlinear Feynman–Kac formula
spellingShingle Kaori Okuma
An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
International Journal of Mathematics for Industry
Itô’s formula
Taylor’s expansion
nonlinear Feynman–Kac formula
title An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
title_full An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
title_fullStr An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
title_full_unstemmed An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
title_short An asymptotic expansion of the solution of a semi-linear partial differential equation implied by a nonlinear Feynman–Kac formula
title_sort asymptotic expansion of the solution of a semi linear partial differential equation implied by a nonlinear feynman kac formula
topic Itô’s formula
Taylor’s expansion
nonlinear Feynman–Kac formula
url https://www.worldscientific.com/doi/10.1142/S2661335224500023
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AT kaoriokuma asymptoticexpansionofthesolutionofasemilinearpartialdifferentialequationimpliedbyanonlinearfeynmankacformula