On explosion time in stochastic differential equations driven by fractional Brownian motion
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909331486670848 |
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| author | Garzon, Johanna Leon, Jorge A. Torres, Soledad Tudor, Ciprian A. Viitasaari, Lauri |
| author_facet | Garzon, Johanna Leon, Jorge A. Torres, Soledad Tudor, Ciprian A. Viitasaari, Lauri |
| contents | In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to tackle the case of non-constant diffusion coefficients not covered in the literature. In addition, we provide an adaptive Euler-type numerical scheme for approximating the explosion time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On explosion time in stochastic differential equations driven by fractional Brownian motion Garzon, Johanna Leon, Jorge A. Torres, Soledad Tudor, Ciprian A. Viitasaari, Lauri Probability 65C30, 65L20, 60H10, 60G22 In this article, we study the explosion time of the solution to autonomous stochastic differential equations driven by the fractional Brownian motion with Hurst parameter $H>1/2$. With the help of the Lamperti transformation, we are able to tackle the case of non-constant diffusion coefficients not covered in the literature. In addition, we provide an adaptive Euler-type numerical scheme for approximating the explosion time. |
| title | On explosion time in stochastic differential equations driven by fractional Brownian motion |
| topic | Probability 65C30, 65L20, 60H10, 60G22 |
| url | https://arxiv.org/abs/2410.00581 |