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arXiv · 0905.0782

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

Jérémie Unterberger
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Abstract

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.

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Jérémie Unterberger. 2009-05-06. Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion. https://arxiv.org/abs/0905.0782

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