On forward and backward SPDEs with non-local boundary conditions
We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the termi...
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| Format: | Journal Article |
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American Institute of Mathematical Sciences
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/34666 |
| _version_ | 1848754285117964288 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the terminal time, initial time and continuously distributed times. For the case of backward equations, this setting covers almost surely periodicity. Uniqueness, solvability and regularity results for the solutions are obtained. Some possible applications to portfolio selection are discussed. |
| first_indexed | 2025-11-14T08:37:59Z |
| format | Journal Article |
| id | curtin-20.500.11937-34666 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:37:59Z |
| publishDate | 2015 |
| publisher | American Institute of Mathematical Sciences |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-346662017-09-13T15:56:20Z On forward and backward SPDEs with non-local boundary conditions Dokuchaev, Nikolai backward SPDEs portfolio selection periodic conditions non-local conditions SPDEs We study linear stochastic partial differential equations of parabolic type with non-local in time or mixed in time boundary conditions. The standard Cauchy condition at the terminal time is replaced by a condition that mixes the random values of the solution at different times, including the terminal time, initial time and continuously distributed times. For the case of backward equations, this setting covers almost surely periodicity. Uniqueness, solvability and regularity results for the solutions are obtained. Some possible applications to portfolio selection are discussed. 2015 Journal Article http://hdl.handle.net/20.500.11937/34666 10.3934/dcds.2015.35.5335 American Institute of Mathematical Sciences fulltext |
| spellingShingle | backward SPDEs portfolio selection periodic conditions non-local conditions SPDEs Dokuchaev, Nikolai On forward and backward SPDEs with non-local boundary conditions |
| title | On forward and backward SPDEs with non-local boundary conditions |
| title_full | On forward and backward SPDEs with non-local boundary conditions |
| title_fullStr | On forward and backward SPDEs with non-local boundary conditions |
| title_full_unstemmed | On forward and backward SPDEs with non-local boundary conditions |
| title_short | On forward and backward SPDEs with non-local boundary conditions |
| title_sort | on forward and backward spdes with non-local boundary conditions |
| topic | backward SPDEs portfolio selection periodic conditions non-local conditions SPDEs |
| url | http://hdl.handle.net/20.500.11937/34666 |