Linganisha mbinu

	Nadharia ya Thamani Iliyokithiri (EVT)	Milinganyo ya Tofauti ya Stokastiki (SDEs)
Nyanja	Fedha	Uigaji
Familia	Regression model	Process / pipeline
Mwaka wa asili	2001	1944 (theory); 1992 (numerical framework)
Mwanzilishi	Coles (textbook treatment); McNeil, Frey & Embrechts	Kiyosi Itô (Itô calculus, 1944); Peter Kloeden & Eckhard Platen (numerical methods, 1992)
Aina	Tail / extreme-event model	Continuous-time stochastic process model
Chanzo asilia	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.
Majina mbadala	EVT, generalized extreme value, generalized Pareto distribution, peaks over threshold	SDE, Itô equations, Stokastik Diferansiyel Denklemler (SDE)
Zinazohusiana	5	4
Muhtasari	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.