Open Access
March 2005 Ergodicity of stochastic differential equations driven by fractional Brownian motion
Martin Hairer
Ann. Probab. 33(2): 703-758 (March 2005). DOI: 10.1214/009117904000000892


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.


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Martin Hairer. "Ergodicity of stochastic differential equations driven by fractional Brownian motion." Ann. Probab. 33 (2) 703 - 758, March 2005.


Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1071.60045
MathSciNet: MR2123208
Digital Object Identifier: 10.1214/009117904000000892

Primary: 26A33 , 60H10

Keywords: ergodicity , fractional Brownian motion , memory

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.33 • No. 2 • March 2005
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