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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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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