Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation
Abstract
This paper investigates the generative mechanism of the p-order cloud model, which is a mathematical framework for representing uncertainty with applications in image processing, evaluation, and decision-making systems. By employing a reparameterization technique, we reformulate the cloud model as a stochastic recurrence equation (SRE) with a nonlinear transformation involving an absolute value. Under standard assumptions of stationarity, ergodicity, and an appropriate integrability condition, we establish the existence and uniqueness of a stationary solution. In particular, we demonstrate that the logarithmic moment of the model's coefficient, modeled as a standard normal random variable, is negative, thereby ensuring almost sure convergence. These results provide new insights into the stochastic stability of cloud models and offer a rigorous foundation for further theoretical and practical developments in uncertainty quantification.
Cite
@article{arxiv.2505.18203,
title = {Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation},
author = {Biao Hu and Minyue Wang},
journal= {arXiv preprint arXiv:2505.18203},
year = {2025}
}