Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation

Biao Hu; Minyue Wang

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arXiv · 2505.18203

Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation

Biao Hu·Minyue Wang

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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.

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BibTeX RIS

Biao Hu, Minyue Wang. 2025-05-21. Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation. https://arxiv.org/abs/2505.18203

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