On probability laws of solutions to differential systems driven by a fractional Brownian motion

• F. Baudoin ^[1] ; E. Nualart ^[2] ; C. Ouyang ^[4] ; S. Tindel ^[3]
  1. [1] Purdue University

     Purdue University

     Township of Wabash, Estados Unidos

     
  2. [2] Universitat Pompeu Fabra

     Universitat Pompeu Fabra

     Barcelona, España

     
  3. [3] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
  4. [4] University of Illinois (Chicago)

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• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 4, 2016, págs. 2554-2590
• Idioma: inglés
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• Resumen

  • This article investigates several properties related to densities of solutions (Xt)t∈[0,1](Xt)t∈[0,1] to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4H>1/4. We first determine conditions for strict positivity of the density of XtXt. 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.