@article{ECP1574,
author = {Jeremie Unterberger},
title = {Moment estimates for solutions of linear stochastic differential equations driven by analytic fractional Brownian motion},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {stochastic differential equations, fractional Brownian motion, analytic fractional Brownian motion, rough paths, H\"older continuity, Chen series},
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.},
pages = {no. 37, 411-417},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1574},
url = {http://ecp.ejpecp.org/article/view/1574}}