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On probability laws of solutions to differential systems driven by a fractional Brownian motion. (English) Zbl 1352.60081
In this paper, differential equations driven by a fractional Brownian motion are considered. Some conditions for strict positivity of the density of solutions are found and exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition are obtained. Some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities are derived.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G22 Fractional processes, including fractional Brownian motion
60H07 Stochastic calculus of variations and the Malliavin calculus
60G15 Gaussian processes
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