Process / pipeline
Stochastic Differential Equations (SDEs)
Stochastic differential equations (SDEs) are differential equation models that combine a deterministic drift term — governing the average tendency of a system — with a stochastic diffusion term driven by a Wiener process (Brownian motion). Pioneered through Itô calculus by Kiyosi Itô in 1944 and given a comprehensive numerical treatment by Kloeden and Platen in 1992, SDEs are the standard modelling language for continuous-time systems subject to random noise, including financial asset prices, population dynamics, and physical processes.
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Sources
- Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI: 10.1007/978-3-642-14394-6 ↗
- Kloeden, P.E. & Platen, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer. DOI: 10.1007/978-3-662-12616-5 ↗