Research on Modeling and Solving Stochastic Equations in Information Systems

This paper investigates the stochastic characteristics in large-scale distributed information systems. By analyzing random phenomena such as system failures, network delays, and server loads, corresponding mathematical models are established. A hierarchical and progressive HSRA (Hierarchical Stochastic Response Analysis) solving framework is designed, incorporating core solving methods like the improved Metropolis-Hastings algorithm, particle filtering, and LSTM neural networks. Experimental results demonstrate that the proposed model excels in tasks such as failure prediction, delay prediction, and load prediction. Through parallel acceleration optimization, the system’s processing capacity is significantly enhanced while maintaining a high level of resource utilization. The research findings provide effective theoretical and technical support for the reliability assessment and performance optimization of information systems.