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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.18203 |
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| _version_ | 1866916756292894720 |
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| author | Hu, Biao Wang, Minyue |
| author_facet | Hu, Biao Wang, Minyue |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18203 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation Hu, Biao Wang, Minyue Optimization and Control 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. |
| title | Stationary Solution of p-Order Cloud Model via Stochastic Recurrence Equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.18203 |