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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| _version_ | 1832576344606638080 |
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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 |