Stochastic Processes

Stochastic Processes describe systems whose evolution involves randomness and probabilistic behavior. Unlike deterministic systems, stochastic systems evolve according to probability distributions rather than fixed trajectories. These processes are used to model noise, uncertainty, and fluctuations in physical systems. Examples include diffusion, random walks, and thermal noise. Stochastic processes are essential in statistical mechanics, condensed matter physics, and non-equilibrium dynamics. They provide tools to analyze systems influenced by environmental randomness. Mathematical formulations involve probability theory and differential equations. Stochastic processes are also widely applied in finance, population dynamics, and biological systems. In physics, they help bridge microscopic randomness and macroscopic laws. Understanding stochastic processes is crucial for modeling real-world systems where uncertainty and fluctuations play a dominant role.