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July 2016 On probability laws of solutions to differential systems driven by a fractional Brownian motion
F. Baudoin, E. Nualart, C. Ouyang, S. Tindel
Ann. Probab. 44(4): 2554-2590 (July 2016). DOI: 10.1214/15-AOP1028

Abstract

This article investigates several properties related to densities of solutions $(X_{t})_{t\in[0,1]}$ to differential equations driven by a fractional Brownian motion with Hurst parameter $H>1/4$. We first determine conditions for strict positivity of the density of $X_{t}$. Then we obtain some exponential bounds for this density when the diffusion coefficient satisfies an elliptic type condition. Finally, still in the elliptic case, we derive some bounds on the hitting probabilities of sets by fractional differential systems in terms of Newtonian capacities.

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F. Baudoin. E. Nualart. C. Ouyang. S. Tindel. "On probability laws of solutions to differential systems driven by a fractional Brownian motion." Ann. Probab. 44 (4) 2554 - 2590, July 2016. https://doi.org/10.1214/15-AOP1028

Information

Received: 1 January 2014; Revised: 1 February 2015; Published: July 2016
First available in Project Euclid: 2 August 2016

zbMATH: 1352.60081
MathSciNet: MR3531675
Digital Object Identifier: 10.1214/15-AOP1028

Subjects:
Primary: 60G15, 60H07, 60H10, 65C30

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 4 • July 2016
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