Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion
Abstract
As a general rule, differential equations driven by a multidimensional 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 Hölder 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 [7, 8] with arbitrary Hurst index $\alpha \in (0, 1)$ may be solved on the closed upper halfplane, and that the solutions have finite variance.
 Publication:

arXiv eprints
 Pub Date:
 May 2009
 DOI:
 10.48550/arXiv.0905.0782
 arXiv:
 arXiv:0905.0782
 Bibcode:
 2009arXiv0905.0782U
 Keywords:

 Mathematics  Probability;
 60G15;
 60H15;
 60H10