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

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.