03-165 Martin Hairer

Ergodicity of Stochastic Differential Equations Driven by Fractional Brownian Motion (450K, PDF) Apr 10, 03

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. 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 towards the stationary one is (at least) algebraic. A lower bound on the exponent is also given.

Files: 03-165.src( 03-165.keywords , fbm.pdf.mm )