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Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions. (English) Zbl 1341.60049

The authors consider the solutions of stochastic differential equations driven by a fractional Brownian motion with Hurst parameter \(H\). They consider both the one-dimensional case with additive noise and the multidimensional case. In the former case they assume \(H\in (0,1)\) and in the latter case \(H\in (0, 1/2)\). The investigation relies on stochastic analysis and on pathwise methods in stochastic differential equations.

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
34K50 Stochastic functional-differential equations
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