Approximation to multifractional Riemann-Liouville Brownian sheet

TL;DR

This paper introduces multifractional Riemann-Liouville Brownian sheets and demonstrates their approximation in law using sequences of i.i.d. random variables, advancing stochastic process modeling.

Contribution

It presents the first approximation results for multifractional Riemann-Liouville Brownian sheets using i.i.d. sequences, expanding the understanding of these complex stochastic processes.

Findings

Established approximation in law for multifractional Riemann-Liouville Brownian sheets

Constructed approximations based on i.i.d. random variables

Extended stochastic process approximation techniques

Abstract

In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence of I.I.D random variables.