Abstract
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.
Citation
Martin Hairer. "Ergodicity of stochastic differential equations driven by fractional Brownian motion." Ann. Probab. 33 (2) 703 - 758, March 2005. https://doi.org/10.1214/009117904000000892
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