On probability laws of solutions to differential systems driven by a fractional Brownian motion
This article investigates several properties related to densities of solutions (Xt)t∈[0,1] to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density of Xt. Then we obtain some exponential bou...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:10230/34392 |
| Acceso en línea: | http://hdl.handle.net/10230/34392 http://dx.doi.org/10.1214/15-AOP1028 |
| Access Level: | acceso abierto |
| Palabra clave: | Fractional Brownian motion Rough paths Malliavin calculus Hitting probability |
| Sumario: | This article investigates several properties related to densities of solutions (Xt)t∈[0,1] to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density of Xt. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities. |
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