応用数理科学における確率的問題<br>Stochastic Calculus : Applications in Science and Engineering

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応用数理科学における確率的問題
Stochastic Calculus : Applications in Science and Engineering

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  • 製本 Hardcover:ハードカバー版／ページ数 700 p.
  • 言語 ENG
  • 商品コード 9780817642426
  • DDC分類 519.2

基本説明

Textbook.

Full Description

Algebraic, differential, and integral equations are used in the applied sciences, en­ gineering, economics, and the social sciences to characterize the current state of a physical, economic, or social system and forecast its evolution in time. Generally, the coefficients of and/or the input to these equations are not precisely known be­ cause of insufficient information, limited understanding of some underlying phe­ nomena, and inherent randonmess. For example, the orientation of the atomic lattice in the grains of a polycrystal varies randomly from grain to grain, the spa­ tial distribution of a phase of a composite material is not known precisely for a particular specimen, bone properties needed to develop reliable artificial joints vary significantly with individual and age, forces acting on a plane from takeoff to landing depend in a complex manner on the environmental conditions and flight pattern, and stock prices and their evolution in time depend on a large number of factors that cannot be described by deterministic models. Problems that can be defined by algebraic, differential, and integral equations with random coefficients and/or input are referred to as stochastic problems. The main objective of this book is the solution of stochastic problems, that is, the determination of the probability law, moments, and/or other probabilistic properties of the state of a physical, economic, or social system. It is assumed that the operators and inputs defining a stochastic problem are specified.

Contents

Introduction * Probability Theory * Stochastic Processes * Itô's Formula and Stochastic Differential Equations * Monte Carlo Simulation * Deterministic System and Input * Deterministic System and Stochastic Input * Stochastic System and Deterministic Input * Stochastic System and Stochastic Input * Bibliography * Index