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2010 Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
Jeremie Unterberger
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Electron. Commun. Probab. 15(none): 411-417 (2010). DOI: 10.1214/ECP.v15-1574

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.

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Jeremie Unterberger. "Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion." Electron. Commun. Probab. 15 411 - 417, 2010. https://doi.org/10.1214/ECP.v15-1574

Information

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

zbMATH: 1226.60091
MathSciNet: MR2726087
Digital Object Identifier: 10.1214/ECP.v15-1574

Subjects:
Primary: 60G15
Secondary: 60H05, 60H10

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