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| نظرية القيم القصوى (EVT)× | المعادلات التفاضلية العشوائية (SDEs)× | |
|---|---|---|
| المجال≠ | التمويل | المحاكاة |
| العائلة≠ | Regression model | Process / pipeline |
| سنة النشأة≠ | 2001 | 1944 (theory); 1992 (numerical framework) |
| صاحب الطريقة≠ | Coles (textbook treatment); McNeil, Frey & Embrechts | Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992) |
| النوع≠ | Tail / extreme-event model | Continuous-time stochastic process model |
| المصدر التأسيسي≠ | Coles, S. (2001). An Introduction to Statistical Modeling of Extreme Values. Springer. ISBN: 978-1852334598 | Øksendal, B. (2003). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer. DOI ↗ |
| الأسماء البديلة≠ | EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold | SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE) |
| ذات صلة≠ | 5 | 4 |
| الملخص≠ | Extreme Value Theory is a statistical framework for modelling the rare events that live in the tail of a probability distribution. As developed in Coles (2001) and applied to risk by McNeil, Frey & Embrechts (2005), it offers two standard routes: the Generalized Extreme Value (GEV) distribution for block maxima and the Generalized Pareto Distribution (GPD), used in the peaks-over-threshold approach, for exceedances above a high threshold. | 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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