Semi-implicit Taylor schemes for stiff rough differential equations
We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the multiplicative noise case, the equation is understood as a ro...
| Main Authors: | , |
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| Format: | Internet publication |
| Language: | English |
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2020
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| _version_ | 1797109995878219776 |
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| author | Riedel, S Wu, Yue |
| author_facet | Riedel, S Wu, Yue |
| author_sort | Riedel, S |
| collection | OXFORD |
| description | We study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the multiplicative noise case, the equation is understood as a rough differential equation in the sense of T.~Lyons. We focus on equations for which the drift coefficient may be unbounded and satisfies a one-sided Lipschitz condition only. We prove well-posedness of the methods, provide a full analysis, and deduce their convergence rate. Numerical experiments show that our schemes are particularly useful in the case of stiff rough stochastic differential equations driven by a fractional Brownian motion. |
| first_indexed | 2024-03-07T07:49:02Z |
| format | Internet publication |
| id | oxford-uuid:cd340e53-a82e-4f46-a36b-b5dc50c731e0 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:49:02Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | oxford-uuid:cd340e53-a82e-4f46-a36b-b5dc50c731e02023-06-21T16:45:17ZSemi-implicit Taylor schemes for stiff rough differential equationsInternet publicationhttp://purl.org/coar/resource_type/c_7ad9uuid:cd340e53-a82e-4f46-a36b-b5dc50c731e0EnglishSymplectic Elements2020Riedel, SWu, YueWe study a class of semi-implicit Taylor-type numerical methods that are easy to implement and designed to solve multidimensional stochastic differential equations driven by a general rough noise, e.g. a fractional Brownian motion. In the multiplicative noise case, the equation is understood as a rough differential equation in the sense of T.~Lyons. We focus on equations for which the drift coefficient may be unbounded and satisfies a one-sided Lipschitz condition only. We prove well-posedness of the methods, provide a full analysis, and deduce their convergence rate. Numerical experiments show that our schemes are particularly useful in the case of stiff rough stochastic differential equations driven by a fractional Brownian motion. |
| spellingShingle | Riedel, S Wu, Yue Semi-implicit Taylor schemes for stiff rough differential equations |
| title | Semi-implicit Taylor schemes for stiff rough differential equations |
| title_full | Semi-implicit Taylor schemes for stiff rough differential equations |
| title_fullStr | Semi-implicit Taylor schemes for stiff rough differential equations |
| title_full_unstemmed | Semi-implicit Taylor schemes for stiff rough differential equations |
| title_short | Semi-implicit Taylor schemes for stiff rough differential equations |
| title_sort | semi implicit taylor schemes for stiff rough differential equations |
| work_keys_str_mv | AT riedels semiimplicittaylorschemesforstiffroughdifferentialequations AT wuyue semiimplicittaylorschemesforstiffroughdifferentialequations |