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Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients /
"Many stochastic differential equations (SDEs) in the literature have a super linearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler Maruyama approximation method diverge for these SDEs in finite time. This article de...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, Rhode Island :
American Mathematical Society,
2015.
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| Colección: | Memoirs of the American Mathematical Society ;
no. 1112. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | "Many stochastic differential equations (SDEs) in the literature have a super linearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete time stochastic processes. Using this approach, we establish moment bounds for fully and partially drift implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, we illustrate our results for several SDEs from finance, physics, biology and chemistry."--Page v |
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| Notas: | "Volume 236, number 1112 (second of 6 numbers), July 2015." |
| Descripción Física: | 1 online resource (v, 99 pages) |
| Bibliografía: | Includes bibliographical references (pages 95-99). |
| ISBN: | 9781470422783 1470422786 |
| ISSN: | 0065-9266, 1947-6221 ; |