We study the ergodic properties of finite-dimensional systems of SDEs driven by nondegenerate additive fractional Brownian motion with arbitrary Hurst parameter H∈(0,1). A general framework is constructed to make precise the notions of “invariant measure” and “stationary state” for such a system. We then prove under rather weak dissipativity conditions that such an SDE possesses a unique stationary solution and that the convergence rate of an arbitrary solution toward the stationary one is (at least) algebraic. A lower bound on the exponent is also given.
@article{1109868598,
author = {Hairer, Martin},
title = {Ergodicity of stochastic differential equations driven by fractional Brownian motion},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 703-758},
language = {en},
url = {http://dml.mathdoc.fr/item/1109868598}
}
Hairer, Martin. Ergodicity of stochastic differential equations driven by fractional Brownian motion. Ann. Probab., Tome 33 (2005) no. 1, pp. 703-758. http://gdmltest.u-ga.fr/item/1109868598/