stochastic differential equations

Stochastic differential equations (SDEs) are mathematical models used to describe systems that evolve over time with inherent randomness, like stock prices or weather patterns. They extend regular differential equations by including a term that accounts for unpredictable, random influences, often represented as "noise." This allows us to capture both predictable trends and randomness simultaneously. SDEs are essential in fields like finance, physics, and biology for modeling complex, uncertain phenomena where uncertainty plays a crucial role in the system's behavior.