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Kramers-Smoluchowski approximation for stochastic evolution equations with FBM. (English) Zbl 1086.60040

Summary: Let \(\{B^H_t,t\in[0,\tau]\}\) be a fractional Brownian motion with Hurst parameter \(H\in(0,1)\). We give a Kramers-Smoluchowski approximation for the solution of the equation \(X_t=x+B^H_t+\int^t_0 b(X_s)\,ds\). The case \(H=1/2\) is the classical situation, which may describe the motion of particles in a fluid.

MSC:

60H20 Stochastic integral equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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