Article2014

Harnack-Type Inequalities and Applications for SDE Driven by Fractional Brownian Motion

15 citations0/0 files storedStochastic Analysis and Applications

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Geometric Analysis and Curvature Flows

Abstract

For stochastic differential equation driven by fractional Brownian motion with Hurst parameter H > 1/2, Harnack-type inequalities are established by constructing a coupling with unbounded time-dependent drift. These inequalities are applied to the study of existence and uniqueness of invariant measure for a discrete Markov semigroup constructed in terms of the distribution of the solution. Furthermore, we show that entropy-cost inequality holds for the invariant measure.

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References

2006The Malliavin Calculus and Related Topics 2008Stochastic Calculus for Fractional Brownian Motion and Applications 1998Differential equations driven by rough signals 1999Stochastic Analysis of the Fractional Brownian Motion 1998Integration with respect to fractal functions and stochastic calculus. I 2001Stochastic Calculus with Respect to Gaussian Processes 2002Differential equations driven by fractional Brownian motion 2002Stochastic analysis, rough path analysis and fractional Brownian motions

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