Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 15 (2010), paper no. 37, 411-417.
Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
As a general rule, differential equations driven by a multi-dimensional irregular path $\Gamma$ are solved by constructing a rough path over $\Gamma$. 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 Holder regularity $\alpha<1/2$. We prove here (by showing convergence of Chen's series) that linear stochastic differential equations driven by analytic fractional Brownian motion [6,7] with arbitrary Hurst index $\alpha\in(0,1)$ may be solved on the closed upper half-plane, and that the solutions have finite variance.
Electron. Commun. Probab., Volume 15 (2010), paper no. 37, 411-417.
Accepted: 30 September 2010
First available in Project Euclid: 6 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G15: Gaussian processes
Secondary: 60H05: Stochastic integrals 60H10: Stochastic ordinary differential equations [See also 34F05]
This work is licensed under aCreative Commons Attribution 3.0 License.
Unterberger, Jeremie. Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion. Electron. Commun. Probab. 15 (2010), paper no. 37, 411--417. doi:10.1214/ECP.v15-1574. https://projecteuclid.org/euclid.ecp/1465243980