stochastic partial differential equations

Stochastic partial differential equations (SPDEs) are mathematical tools used to model systems that evolve over space and time with inherent randomness or noise. Unlike traditional equations that predict a single outcome, SPDEs account for unpredictable factors—like weather variability or fluctuating financial markets—by incorporating random elements. They help describe complex phenomena where uncertainty plays a central role, providing a framework for understanding and predicting behaviors in fields such as physics, finance, and biology where both spatial structure and randomness are important.