Matrix-analytic Methods in Stochastic Models

隨機微分方程已廣泛用於金融數量計算，如利率期限結構，資產定價以及金融衍生品定價等。隨機微分方程是金融數學的一個重要理論工具，而設計快速有效的算法求解金融隨機模型的複雜隨機微分方程和模型的參數校準是非常重要的兩個問題，解決這類問題對相關金融數學理論的發展也具有重要的推動作用。本書設計一類高階算法對列維過程驅動的隨機微分方程和延遲隨機微分方程求解並將其應用于期權定價研究，並且還設計一類基於粒子群優化的

Since its first appearance as a set of lecture notes published by the Courant Institute in 1974, this book has served as an introduction to various subjects in nonlinear functional analysis. The current edition is a reprint of these notes, with added bibliographic references.Topological and analytic methods are developed for treating nonlinear ordinary and partial differential equations. The first two chapters of the book introduce the notion of topological degree and develop its basic properties. These properties are used in later chapters in the discussion of bifurcation theory （the possible branching of solutions as parameters vary）, including the proof of Rabinowitz's global bifurcation theorem. Stability of the branches is also studied. The book concludes with a presentation of some generalized implicit function theorems of Nash-Moser type with applications to Kolmogorov-Arnold-Moser theory and to conjugacy problems.After more than 20 years, this book continues to be an excellent

《代數幾何中的解析方法(英文版)》內容簡介：This volume is an expansion of lectures given by the author at the Park City Mathematics Institute in 2008 as well as in other places. The main purpose of the book is to describe

Multilevel Models: Appfications Using SAS is written in nontechnical terms, focuses on the methods and applications of various multilevel models, including liner multilevel models,multilevel logistic