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| Équations Différentielles Stochastiques (EDS)× | Simulation de Monte-Carlo× | |
|---|---|---|
| Domaine≠ | Simulation | Prise de décision |
| Famille≠ | Process / pipeline | MCDM |
| Année d'origine≠ | 1944 (theory); 1992 (numerical framework) | 1949 |
| Auteur d'origine≠ | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) | Metropolis, N., Ulam, S. |
| Type≠ | Continuous-time stochastic process model | Robustness wrapper — Monte Carlo uncertainty propagation |
| Source fondatrice≠ | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ | Metropolis, N., Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association DOI ↗ |
| Alias≠ | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) | — |
| Apparentées≠ | 4 | 0 |
| Résumé≠ | 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. | MONTE-CARLO-SIMULATION (Monte Carlo Simulation — Stochastic uncertainty propagation through MCDM model) is a ranking multi-criteria decision-making (MCDM) method introduced by Metropolis, N., Ulam, S. in 1949. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result. |
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