Local times for multifractional Brownian motion in higher dimensions: A white noise approach

TL;DR

This paper develops a white noise approach to express and analyze the local times of multifractional Brownian motion in higher dimensions, establishing their existence and convergence in the framework of generalized white noise functionals.

Contribution

It introduces a novel white noise expansion for mBm local times in higher dimensions and proves their convergence as Hida distributions.

Findings

Existence of local times in higher dimensions via Wick powers

Convergence of regularized local times in Hida distribution sense

Extension of white noise techniques to multifractional processes

Abstract

We present the expansion of the multifractional Brownian (mBm) local time in higher dimensions, in terms of Wick powers of white noises (or multiple Wiener integrals). If a suitable number of kernels is subtracted, they exist in the sense of generalized white noise functionals. Moreover we show the convergence of the regularized truncated local times for mBm in the sense of Hida distributions.