Efficient and practical implementations of cubature on wiener space
This paper explores and implements high-order numerical schemes for integrating linear parabolic partial differential equations with piece-wise smooth boundary data. The high-order Monte-Carlo methods we present give extremely accurate approximations in computation times that we believe are comparab...
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| Format: | Book section |
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Springer Berlin Heidelberg
2011
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| _version_ | 1797099330519171072 |
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| author | Gyurkó, L Lyons, T |
| author_facet | Gyurkó, L Lyons, T |
| author_sort | Gyurkó, L |
| collection | OXFORD |
| description | This paper explores and implements high-order numerical schemes for integrating linear parabolic partial differential equations with piece-wise smooth boundary data. The high-order Monte-Carlo methods we present give extremely accurate approximations in computation times that we believe are comparable with much less accurate finite difference and basic Monte-Carlo schemes. A key step in these algorithms seems to be that the order of the approximation is tuned to the accuracy one requires. A considerable improvement in efficiency can be attained by using ultra high-order cubature formulae. Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169-198) give a degree 5 approximation of Brownian motion. We extend this cubature to degrees 9 and 11 in 1-dimensional space-time. The benefits are immediately apparent. © 2011 Springer-Verlag Berlin Heidelberg. |
| first_indexed | 2024-03-07T05:22:17Z |
| format | Book section |
| id | oxford-uuid:df55110b-9725-4def-b00d-0f71153b950b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:22:17Z |
| publishDate | 2011 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | oxford-uuid:df55110b-9725-4def-b00d-0f71153b950b2022-03-27T09:38:41ZEfficient and practical implementations of cubature on wiener spaceBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:df55110b-9725-4def-b00d-0f71153b950bSymplectic Elements at OxfordSpringer Berlin Heidelberg2011Gyurkó, LLyons, TThis paper explores and implements high-order numerical schemes for integrating linear parabolic partial differential equations with piece-wise smooth boundary data. The high-order Monte-Carlo methods we present give extremely accurate approximations in computation times that we believe are comparable with much less accurate finite difference and basic Monte-Carlo schemes. A key step in these algorithms seems to be that the order of the approximation is tuned to the accuracy one requires. A considerable improvement in efficiency can be attained by using ultra high-order cubature formulae. Lyons and Victoir (Cubature on Wiener Space, Proc. R. Soc. Lond. A 460, 169-198) give a degree 5 approximation of Brownian motion. We extend this cubature to degrees 9 and 11 in 1-dimensional space-time. The benefits are immediately apparent. © 2011 Springer-Verlag Berlin Heidelberg. |
| spellingShingle | Gyurkó, L Lyons, T Efficient and practical implementations of cubature on wiener space |
| title | Efficient and practical implementations of cubature on wiener space |
| title_full | Efficient and practical implementations of cubature on wiener space |
| title_fullStr | Efficient and practical implementations of cubature on wiener space |
| title_full_unstemmed | Efficient and practical implementations of cubature on wiener space |
| title_short | Efficient and practical implementations of cubature on wiener space |
| title_sort | efficient and practical implementations of cubature on wiener space |
| work_keys_str_mv | AT gyurkol efficientandpracticalimplementationsofcubatureonwienerspace AT lyonst efficientandpracticalimplementationsofcubatureonwienerspace |