DEVELOPMENT OF STOCHASTIC MODELS FOR ANALYZING RANDOM PROCESSES AND THEIR APPLICATIONS IN MODERN PHYSICS

Abstract

Stochastic models provide a fundamental mathematical framework for analyzing random processes in modern physics, bridging microscopic fluctuations with macroscopic phenomena. This review traces the historical development from Einstein’s and Langevin’s foundational work on Brownian motion to contemporary applications in stochastic thermodynamics, open quantum systems, stochastic quantization (Parisi-Wu method), and the detection of stochastic gravitational wave backgrounds via pulsar timing arrays. Key mathematical tools include Fokker-Planck equations, Ito/Stratonovich interpretations of stochastic differential equations, fluctuation theorems, and unraveling techniques for density matrix evolution. These models enable the study of non-equilibrium systems, multiple exciton generation, decoherence in quantum systems, and non-Markovian dynamics. Integration with machine learning via physics-informed neural networks and emerging hardware implementations further expands their utility. Stochastic approaches are essential for understanding complex systems in statistical mechanics, quantum field theory, biophysics, and cosmology, offering predictive power where deterministic models fail.