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March 2022 Precise local estimates for differential equations driven by fractional Brownian motion: Hypoelliptic case
Xi Geng, Cheng Ouyang, Samy Tindel
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Ann. Probab. 50(2): 649-687 (March 2022). DOI: 10.1214/21-AOP1542

Abstract

This article is concerned with stochastic differential equations driven by a d dimensional fractional Brownian motion with Hurst parameter H>1/4 and understood in the rough paths sense. Whenever the coefficients of the equation satisfy a uniform hypoellipticity 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. Our methodology relies heavily on the rough paths structure of the equation.

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Xi Geng. Cheng Ouyang. Samy Tindel. "Precise local estimates for differential equations driven by fractional Brownian motion: Hypoelliptic case." Ann. Probab. 50 (2) 649 - 687, March 2022. https://doi.org/10.1214/21-AOP1542

Information

Received: 1 August 2020; Published: March 2022
First available in Project Euclid: 24 March 2022

Digital Object Identifier: 10.1214/21-AOP1542

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

Keywords: fractional Brownian motion , Malliavin calculus , Rough paths

Rights: Copyright © 2022 Institute of Mathematical Statistics

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Vol.50 • No. 2 • March 2022
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