The asymptotic error of chaos expansion approximations for stochastic differential equations
In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. W...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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VTeX
2019-04-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://www.vmsta.org/doi/10.15559/19-VMSTA133 |
| _version_ | 1828772212509769728 |
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| author | Tony Huschto Mark Podolskij Sebastian Sager |
| author_facet | Tony Huschto Mark Podolskij Sebastian Sager |
| author_sort | Tony Huschto |
| collection | DOAJ |
| description | In this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus. |
| first_indexed | 2024-12-11T14:39:35Z |
| format | Article |
| id | doaj.art-c2979bcc314f43a2b50c79e73a58822d |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-11T14:39:35Z |
| publishDate | 2019-04-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-c2979bcc314f43a2b50c79e73a58822d2022-12-22T01:01:59ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542019-04-016214516510.15559/19-VMSTA133The asymptotic error of chaos expansion approximations for stochastic differential equationsTony Huschto0Mark Podolskij1Sebastian Sager2Department of Mathematics, Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, GermanyDepartment of Mathematics, Aarhus University, Ny Munkegade 118, 8000 Aarhus, DenmarkFaculty of Mathematics, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, GermanyIn this paper we present a numerical scheme for stochastic differential equations based upon the Wiener chaos expansion. The approximation of a square integrable stochastic differential equation is obtained by cutting off the infinite chaos expansion in chaos order and in number of basis elements. We derive an explicit upper bound for the ${L^{2}}$ approximation error associated with our method. The proofs are based upon an application of Malliavin calculus.https://www.vmsta.org/doi/10.15559/19-VMSTA133Chaos expansionMalliavin calculusnumerical approximationStochastic differential equations |
| spellingShingle | Tony Huschto Mark Podolskij Sebastian Sager The asymptotic error of chaos expansion approximations for stochastic differential equations Modern Stochastics: Theory and Applications Chaos expansion Malliavin calculus numerical approximation Stochastic differential equations |
| title | The asymptotic error of chaos expansion approximations for stochastic differential equations |
| title_full | The asymptotic error of chaos expansion approximations for stochastic differential equations |
| title_fullStr | The asymptotic error of chaos expansion approximations for stochastic differential equations |
| title_full_unstemmed | The asymptotic error of chaos expansion approximations for stochastic differential equations |
| title_short | The asymptotic error of chaos expansion approximations for stochastic differential equations |
| title_sort | asymptotic error of chaos expansion approximations for stochastic differential equations |
| topic | Chaos expansion Malliavin calculus numerical approximation Stochastic differential equations |
| url | https://www.vmsta.org/doi/10.15559/19-VMSTA133 |
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