方法对比

	蒙特卡洛模拟的方差缩减技术	随机微分方程 (SDEs)
领域	仿真	仿真
方法族	Process / pipeline	Process / pipeline
起源年份	1950s–1980s (technique family)	1944 (theory); 1992 (numerical framework)
提出者	Hammersley & Morton (antithetic variates, 1956); Lavenberg & Welch (control variates, 1981); importance sampling roots in Kahn & Marshall (1953)	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
类型	Simulation variance-reduction technique family	Continuous-time stochastic process model
开创性文献	Ross, S.M. (2012). Simulation (5th ed.). Academic Press. ISBN: 978-0124158252	Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.
别名	antithetic variates, control variates, importance sampling, stratified sampling MC	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
相关	4	4
摘要	Variance reduction techniques are a family of methods that improve the efficiency of Monte Carlo simulation by achieving the same estimation accuracy with fewer random draws. Developed incrementally from the 1950s onward — with antithetic variates attributed to Hammersley and Morton, control variates formalised by Lavenberg and Welch, and importance sampling rooted in Kahn and Marshall — the family includes antithetic variates (AV), control variates (CV), importance sampling (IS), and stratification, each exploiting a different structural property of the target quantity to lower estimator variance without introducing bias.	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.