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Mathematics - Probability Theory and Stochastic Processes | Modeling with Itô Stochastic Differential Equations

Modeling with Itô Stochastic Differential Equations

Allen, E.

2007, XII, 230 p.

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  • Thoroughly explains a procedure for constructing realistic stochastic differential equation models
  • Develops many stochastic differential equation models for randomly varying systems in biology, physics, and finance
  • Explains random variables, stochastic processes, stochastic integration, and stochastic differential equations in a Hilbert space setting, which unifies and simplifies the presentation
  • Many interesting exercises and computer programs provided throughout the text

Dynamical systems with random influences occur throughout the physical, biological, and social sciences. A discrete stochastic process model can be constructed by carefully studying a randomly varying system over a small time interval. Next, an Ito stochastic differential equation model for the dynamical system can be obtained by letting the time interval shrink to zero.

This book thoroughly explains and illustrates this modeling procedure for randomly varying systems in population biology, chemistry, physics, engineering, and finance. Introductory chapters present the fundamental concepts of random variables, stochastic processes, stochastic integration, and stochastic differential equations. These concepts are explained in a Hilbert space setting which unifies and simplifies the presentation. Computer programs, given throughout the text, are useful in solving representative stochastic problems. Each chapter provides analytical and computational exercises that complement the material in the text.

Content Level » Research

Keywords » Probability theory - Random variable - Stochastic processes - dynamische Systeme - model - modeling - programming - stochastic - stochastic process

Related subjects » Analysis - Applications - Computational Science & Engineering - Mathematics - Probability Theory and Stochastic Processes

Table of contents 

Random Variables.- Stochastic Processes.- Stochastic Integration.- Stochastic Differential Equations.- Modeling.

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