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.

References in corpus (9)

• Renormalized self-intersection local time for fractional Brownian motion
• Self-avoiding fractional Brownian motion - The Edwards model
• Intersection local times of independent fractional Brownian motions as generalized white noise functionals
• Derivative for the intersection local time of fractional Brownian Motions
• Chaos Decomposition and Gap Renormalization of Brownian Self-Intersection Local Times
• Renormalization and convergence in law for the derivative of intersection local time in R^2
• Higher-order Derivative Local Time for Fractional Ornstein-Uhlenbeck Processes
• Derivatives of local times for some Gaussian fields
• The spans in Brownian motion

Cited by in corpus (1)

• Existence and Hölder continuity conditions for self-intersection local time of Rosenblatt process