# Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

## TL;DR

This paper develops wavelet-based models to simulate specific classes of stochastic processes, such as powers and products of sub-Gaussian processes, with guaranteed accuracy and reliability in $L_p$ spaces.

## Contribution

It introduces novel wavelet-based simulation methods for processes expressed as powers or products of sub-Gaussian processes, ensuring specified accuracy and reliability.

## Key findings

- Model for $Y(t)=(X(t))^s$ with guaranteed accuracy.
- Model for $Z(t)=X_1(t)X_2(t)$ with specified reliability.
- Applicable in $L_p([0,T])$ for certain classes of processes.

## Abstract

We consider stochastic processes $Y(t)$ which can be represented as $Y(t)=(X(t))^s, s \in \mathbb{N},$ where $X(t)$ is a stationary strictly sub-Gaussian process and build a wavelet-based model that simulates $Y(t)$ with given accuracy and reliability in $L_p([0,T])$. A model for simulation with given accuracy and reliability in $L_p([0,T])$ is also built for processes $Z(t)$ which can be represented as $Z(t)=X_1(t) X_2(t)$, where $X_1(t)$ and $X_2(t)$ are independent stationary strictly sub-Gaussian processes.