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.


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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