Gaussian-type lower bounds for the density of solutions of SDEs driven by fractional Brownian motions

• Besalú, M. ^[2] ; Kohatsu-Higa, A ^[1] ; Tindel, S. ^[2]
  1. [1] Ritsumeikan University

     Ritsumeikan University

     Kamigyō-ku, Japón

     
  2. [2] University of Lorraine

     University of Lorraine

     Arrondissement de Nancy, Francia

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 399-443
• Idioma: inglés
• DOI: 10.1214/14-AOP977
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• Resumen

  • In this paper we obtain Gaussian-type lower bounds for the density of solutions to stochastic differential equations (SDEs) driven by a fractional Brownian motion with Hurst parameter H. In the one-dimensional case with additive noise, our study encompasses all parameters H∈(0,1), while the multidimensional case is restricted to the case H>1/2. We rely on a mix of pathwise methods for stochastic differential equations and stochastic analysis tools.