A Multiplicative Wavelet-based Model for Simulation of a Random Process

TL;DR

This paper introduces a wavelet-based model for simulating a specific type of random process, providing convergence rates for the model when the underlying process is sub-Gaussian.

Contribution

It develops a multiplicative wavelet representation for the exponential of a second-order process and establishes convergence rates for simulation.

Findings

Wavelet-based representation for $Y(t)$ is derived.

Convergence rates are established in $C([0,T])$ and $L_p([0,T])$ spaces.

Model effectively simulates the process $Y(t)$ with quantifiable accuracy.

Abstract

We consider a random process $Y(t)=\exp\{X(t)\}$, where $X(t)$ is a centered second-order process which correlation function $R(t,s)$ can be represented as $\int_{\mathbb{R}} u(t,y)\overline{u(s,y)} dy.$ A multiplicative wavelet-based representation is found for $Y(t)$. We propose a model for simulation of the process $Y(t)$ and find its rates of convergence to the process in the spaces $C([0,T])$ and $L_p([0,T])$ for the case when $X(t)$ is a strictly sub-Gaussian process.