Stochastic systems are processes that involve randomness and uncertainty. Unlike deterministic systems, where outcomes are predictable, stochastic systems can produce different results even under the same initial conditions. This randomness is often modeled using probability theory, allowing for the analysis of various possible outcomes. These systems are commonly found in fields such as finance, biology, and engineering. For example, in finance, stock prices can be influenced by numerous unpredictable factors, making them a classic example of a stochastic system. Understanding these systems helps researchers and professionals make informed decisions despite inherent uncertainties.