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2022 Quasi-sure non-self-intersection for rough differential equations driven by fractional Brownian motion
Cheng Ouyang, William Roberson-Vickery
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Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP454

Abstract

In this paper we study the self-intersection of paths solving elliptic stochastic differential equations driven by fractional Brownian motion. We show that such a path has no self-intersection – except for paths forming a set of zero (r,q)-capacity in the sample space – provided the dimension d of the space and the Hurst parameter H satisfy the inequality d>rq+2H. This inequality is sharp in the case of brownian motion and fractional brownian motion according to existing results. Various results exist for the critical case where d=rq+4 for Brownian motion.

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Cheng Ouyang. William Roberson-Vickery. "Quasi-sure non-self-intersection for rough differential equations driven by fractional Brownian motion." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP454

Information

Received: 2 November 2021; Accepted: 12 February 2022; Published: 2022
First available in Project Euclid: 2 March 2022

Digital Object Identifier: 10.1214/22-ECP454

Subjects:
Primary: 60H07 , 60H10 , 60L20

Keywords: capacity , fractional Brownian motion , Malliavin calculus , rough differential equations , Stochastic differential equations

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