Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
| dc.creator | Unterberger, Jérémie | |
| dc.date | 2009-05-06 | |
| dc.date.accessioned | 2026-07-07T13:12:14Z | |
| dc.date.available | 2026-07-07T13:12:14Z | |
| dc.description | As a general rule, differential equations driven by a multi-dimensional irregular path $Γ$ are solved by constructing a rough path over $Γ$. The domain of definition ? and also estimates ? of the solutions depend on upper bounds for the rough path; these general, deterministic estimates are too crude to apply e.g. to the solutions of stochastic differential equations with linear coefficients driven by a Gaussian process with Hölder regularity $α< 1/2$. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [7, 8] with arbitrary Hurst index $α\in (0, 1)$ may be solved on the closed upper halfplane, and that the solutions have finite variance. | |
| dc.identifier | https://arxiv.org/abs/0905.0782 | |
| dc.identifier | http://arxiv.org/abs/0905.0782 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229522 | |
| dc.subject | Probability | |
| dc.subject | 60G15 ; 60H15 ; 60H10 | |
| dc.title | Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion | |
| dc.type | text |