Electronic Communications in Probability

Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion

Jeremie Unterberger

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Abstract

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.

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 37, 411-417.

Dates
Accepted: 30 September 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243980

Digital Object Identifier
doi:10.1214/ECP.v15-1574

Mathematical Reviews number (MathSciNet)
MR2726087

Zentralblatt MATH identifier
1226.60091

Subjects
Primary: 60G15: Gaussian processes
Secondary: 60H05: Stochastic integrals 60H10: Stochastic ordinary differential equations [See also 34F05]

Keywords
stochastic differential equations fractional Brownian motion analytic fractional Brownian motion rough paths H"older continuity Chen series

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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


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References

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