Existence, renormalization, and regularity properties of higher order derivatives of self-intersection local time of fractional Brownian motion

Abstract

In a recent paper by Yu (arXiv:2008.05633, 2020), higher order derivatives of self-intersection local time of fractional Brownian motion were defined, and existence over certain regions of the Hurst parameter $H$ was proved. Utilizing the Wiener chaos expansion, we provide new proofs of Yu's results, and show how a Varadhan-type renormalization can be used to extend the range of convergence for the even derivatives.