Newton's method for stochastic differential equations and its probabilistic second-order error estimate
Kawabata and Yamada [5] proposed an implicit Newton's method for nonlinear stochastic differential equations and proved its convergence. Later Amano [2] gave an explicit formulation of method and showed its direct error estimate. In this article, we prove a probabilistic second-order error...
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| Format: | Article |
| Language: | English |
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Texas State University
2012-01-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/03/abstr.html |
| Summary: | Kawabata and Yamada [5] proposed an implicit Newton's method for nonlinear stochastic differential equations and proved its convergence. Later Amano [2] gave an explicit formulation of method and showed its direct error estimate. In this article, we prove a probabilistic second-order error estimate which has been an open problem since 1991. |
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| ISSN: | 1072-6691 |