This item is in: Mathematics > Applied mathematics

Stochastic differential equations and applications (Second edition)

X Mao, Strathclyde University, UK

A helpful book for both experts and beginners in pure and applied mathematics, and in probability theory, systems dynamics, and control theory. An enjoyable read.
(Review of the first edition) Professor Martynuk, Ukraine Academy of Sciences

… a welcome and important addition to stochastic differential equations. … giving a clear presentation of the fundamental underpinnings of stochastic differential equations [including the] known theory. … also the development of new results and methods. … Both the depth and breadth of the coverage are remarkable.
Professor G.G. Yin, Wayne State University, USA

 - has been revised and updated to cover the basic principles and applications of various types of stochastic systems
 - useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists

This advanced undergraduate and graduate text has now been revised and updated to cover the basic principles and applications of various types of stochastic systems, with much on theory and applications not previously available in book form. The text is also useful as a reference source for pure and applied mathematicians, statisticians and probabilists, engineers in control and communications, and information scientists, physicists and economists.

ISBN 1 904275 34 6
ISBN-13: 978 1 904275 34 3
December 2007
440 pages  234 x 156mm  paperback  
£50.00 / US$85.00 / €60.00

Usually dispatched within 24 hours

An e-book version of this title is available to purchase as part of a Collection or Pick n Mix or by Chapter. Visit Woodhead Publishing Online

About the author

Xuerong Mao, Strathclyde University, UK

Titles which may also be of interest:
Ordinary differential equations and applications
Linear differential and difference equations
Decision and discrete mathematics
Calculus
A mathematical kaleidoscope

Contents

Brownian motion and stochastic integrals
 - Introduction
 - Basic notations of probability theory
 - Stochastic processes
 - Brownian motions
 - Stochastic integrals
 - Ito’s formula
 - Moment inequalities
 - Gronwall-type inequalities

Stochastic differential equations
 - Introduction
 - Stochastic differential equations
 - Existence and uniqueness of solutions
 - Lp estimates
 - Almost surely asymptotic estimates
 - Caratheodory’s approximate solutions
 - Euler--Maruyama’s approximate solutions
 - SDE and PDE: Feynman-Kac’s formula
 - Solutions as Markov processes

Linear stochastic differential equations
 - Introduction
 - Stochastic Liouville’s formula
 - The variation-of formula
 - Case studies
 - Examples

Stability of stochastic differential equations
 - Introduction
 - Stability in probability
 - Almost sure exponential stability
 - Moment exponential stability
 - Stochastic stabilization and destabilization
 - Further topics

Stochastic functional differential equations
 - Introduction
 - Existence-and-uniqueness theorems
 - Stochastic differential delay equations
 - Exponential estimates
 - Approximate solutions
 - Stability theory-Razunnkhin theorems
 - Stochastic self-stabilization

Stochastic equations of neutral type
 - Neutral stochastic functional differential equations
 - Neutral stochastic differential delay solutions
 - Moment and pathwise estimates
 - Lp--continuity
 - Exponential stability

Backward stochastic differential equations
 - Introduction
 - Martingale representation theorem
 - Equations with Lipscbitz coefficients
 - Equations with non-Lipschitz coefficients
 - Regularities
 - BSDE and quasilinear PDE

Stochastic oscillators
 - Introduction
 - The Cameron-Martin-Girsanov theorem
 - Nonlinear stochastic oscillators
 - Linear stochastic oscillators
 -  Energy bounds

Applications to economics and finance
 - Introduction
 - Stochastic modelling in asset prices
 - Options and their values
 - Optimal stopping problems
 - Stochastic games

Stochastic neural networks
 - Introduction
 - Stochastic neural networks
 - Stochastic neural networks with delays

Stochastic delay population systems
 - Introduction
 - Noise independent of population sizes
 - Noise dependent on population sizes: Part I
 - Noise dependent on population sizes: Part II
 - Stochastic delay Lotka-Volterra food chain

Bibliographical notes

References