Discretization of Stationary Solutions of Stochastic Systems Driven by Fractional Brownian Motion
Journal Article
·
· Applied Mathematics and Optimization
- Johann Wolfgang Goethe-Universitaet, Institut fuer Mathematik (Germany)
In this article we study the behavior of dissipative systems with additive fractional noise of any Hurst parameter. Under a one-sided dissipative Lipschitz condition on the drift the continuous stochastic system is shown to have a unique stationary solution, which pathwise attracts all other solutions. The same holds for the discretized stochastic system, if the drift-implicit Euler method is used for the discretization. Moreover, the unique stationary solution of the drift-implicit Euler scheme converges to the unique stationary solution of the original system as the stepsize of the discretization decreases.
- OSTI ID:
- 21241846
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 60; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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