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| Sztochasztikus differenciálegyenletek (SDE)× | Markov Chain Monte Carlo (MCMC)× | |
|---|---|---|
| Tudományterület | Szimuláció | Szimuláció |
| Módszercsalád | Process / pipeline | Process / pipeline |
| Keletkezés éve≠ | 1944 (theory); 1992 (numerical framework) | 1953 (Metropolis-Hastings); 1984 (Gibbs) |
| Megalkotó≠ | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) | Metropolis et al. (1953); Gibbs sampler formalised by Geman & Geman (1984) |
| Típus≠ | Continuous-time stochastic process model | Simulation-based Bayesian inference / numerical integration |
| Alapmű≠ | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ | Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A. & Rubin, D.B. (2013). Bayesian Data Analysis (3rd ed.). Chapman & Hall/CRC. DOI ↗ |
| Alternatív nevek≠ | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) | MCMC, Metropolis-Hastings, Gibbs sampling, Markov Zinciri Monte Carlo (MCMC — Metropolis-Hastings, Gibbs) |
| Kapcsolódó≠ | 4 | 5 |
| Összefoglaló≠ | 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. | Markov Chain Monte Carlo (MCMC) is a family of simulation algorithms that constructs a Markov chain whose stationary distribution is the target posterior, enabling Bayesian inference and high-dimensional integral computation that would otherwise be analytically intractable. Pioneered by Metropolis and colleagues in 1953 and extended by Hastings in 1970, MCMC underpins modern Bayesian statistics. The two most widely used variants are Metropolis-Hastings, which proposes moves from a general proposal distribution, and Gibbs sampling, which draws each parameter in turn from its full conditional distribution. |
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