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Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case

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Abstract

This article is concerned with stochastic differential equations driven by a d-dimensional fractional Brownian motion with Hurst parameter \(H>1/4\), understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform ellipticity condition, we establish a sharp local estimate on the associated control distance function and a sharp local lower estimate on the density of the solution.

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Authors and Affiliations

  1. School of Mathematics and Statistics, University of Melbourne, Melbourne, Australia

    Xi Geng

  2. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, USA

    Cheng Ouyang

  3. Department of Mathematics, Purdue University, West Lafayette, USA

    Samy Tindel

Authors
  1. Xi Geng
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  2. Cheng Ouyang
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  3. Samy Tindel
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Correspondence to Cheng Ouyang.

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Geng, X., Ouyang, C. & Tindel, S. Precise Local Estimates for Differential Equations driven by Fractional Brownian Motion: Elliptic Case. J Theor Probab 36, 1341–1367 (2023). https://doi.org/10.1007/s10959-022-01208-7

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  • DOI: https://doi.org/10.1007/s10959-022-01208-7

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