方法对比

	不确定性量化	随机微分方程 (SDEs)
领域	仿真	仿真
方法族	Process / pipeline	Process / pipeline
起源年份	Seminal modern form: 2002	1944 (theory); 1992 (numerical framework)
提出者	Norbert Wiener (polynomial chaos, 1938); extended to Wiener–Askey scheme by Xiu & Karniadakis (2002)	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
类型	Computational uncertainty analysis framework	Continuous-time stochastic process model
开创性文献	Xiu, D. & Karniadakis, G.E. (2002). The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 24(2), 619–644.	Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.
别名	UQ, polynomial chaos expansion, PCE, Kriging surrogate	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
相关	9	4
摘要	Uncertainty Quantification (UQ) is a computational framework for systematically measuring how uncertainty in the inputs of a model propagates into uncertainty in its outputs. Building on Wiener's polynomial chaos theory (1938) and formalised for general stochastic problems by Xiu and Karniadakis (2002), UQ uses two primary strategies: Polynomial Chaos Expansion (PCE), which represents the model output as a series of orthogonal polynomials matched to the input distributions, and Kriging (Gaussian process) surrogates, which replace an expensive simulation with a fast statistical approximation fitted to a small set of carefully chosen runs.	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.