Vertaile menetelmiä
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| Varianssin pienentämisen tekniikat Monte Carlo -simulaatioon× | Stokastiset differentiaaliyhtälöt (SDE:t)× | |
|---|---|---|
| Tieteenala | Simulointi | Simulointi |
| Menetelmäperhe | Process / pipeline | Process / pipeline |
| Syntyvuosi≠ | 1950s–1980s (technique family) | 1944 (theory); 1992 (numerical framework) |
| Kehittäjä≠ | 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) |
| Tyyppi≠ | Simulation variance-reduction technique family | Continuous-time stochastic process model |
| Alkuperäislähde≠ | 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. DOI ↗ |
| Rinnakkaisnimet≠ | antithetic variates, control variates, importance sampling, stratified sampling MC | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| Liittyvät | 4 | 4 |
| Tiivistelmä≠ | 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. |
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