Discretization of integrals driven by multifractional Brownian motions with discontinuous integrands

TL;DR

This paper investigates the convergence rate of numerical approximations for stochastic integrals with discontinuous integrands driven by multifractional Brownian motion, extending previous results for fractional Brownian motion.

Contribution

It provides new convergence rate results for integrals driven by multifractional Brownian motion with discontinuous integrands, generalizing prior work on fractional Brownian motion.

Findings

Established the $L^1$-norm convergence rate for approximations

Extended known results from fractional to multifractional Brownian motion

Applicable to integrals with discontinuous integrands

Abstract

We establish the rate of convergence in the $L^1$-norm for equidistant approximations of stochastic integrals with discontinuous integrands driven by multifractional Brownian motion. Our findings extend the known results for the case when the driver is a fractional Brownian motion.