Algorithm for Modelling Stochastic Systems Using Dynamic Probabilistic Automata

This paper presents a novel approach to modeling stochastic systems using Dynamic Probabilistic Automata (DPA), which integrates deterministic and stochastic elements within a unified framework. Traditional methods, such as Markov chains or mass service systems, often struggle with high-dimensional state spaces and complex interactions. DPA overcomes these limitations by enabling flexible modeling of systems with a high degree of uncertainty. It combines probabilistic transitions, deterministic rules, and external influences, making it suitable for diverse applications in biology, economics, physics, and beyond. The proposed methodology supports custom interaction rules, scenario forecasting, and computational optimization. It includes a hierarchical structure that connects stochastic processes, individual object properties, and aggregated meta-states, culminating in a global “world” model. This layered design enables the modeling of complex phenomena, such as rare events, dynamic environmental influences, and high-dimensional interactions. An important feature is DPA's ability to address inverse modeling problems, identifying potential configurations and rules leading to specific outcomes. This has significant implications for decision support systems, optimization tasks, and risk analysis. Future work involves enhancing this framework with big data capabilities, machine learning for parameter calibration, and parallel computing for real-time applications. The flexibility and adaptability of the DPA approach establish it as a powerful tool for advancing our understanding and management of complex systems under uncertainty.