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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Format: | Article |
Language: | English |
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World Scientific Publishing
2024-12-01
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Series: | International Journal of Mathematics for Industry |
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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 |
id | doaj-art-74073fc62ed347e1a49e75b461316a31 |
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 |
work_keys_str_mv | AT kaoriokuma anasymptoticexpansionofthesolutionofasemilinearpartialdifferentialequationimpliedbyanonlinearfeynmankacformula AT kaoriokuma asymptoticexpansionofthesolutionofasemilinearpartialdifferentialequationimpliedbyanonlinearfeynmankacformula |