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 -capacity in the sample space – provided the dimension d of the space and the Hurst parameter H satisfy the inequality . 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 for Brownian motion.
"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