Overview

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.

Full Product Details

Author:   X Mao (Strathclyde University, UK)
Publisher:   Elsevier Science & Technology
Imprint:   Horwood Publishing Ltd
Edition:   2nd edition
Dimensions:   Width: 15.60cm , Height: 2.40cm , Length: 23.40cm
Weight:   0.660kg
ISBN:  

9781904275343

ISBN 10:   1904275346
Pages:   440
Publication Date:   30 December 2007
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

DedicationPreface to the Second EditionPreface from the 1997 Edition AcknowledgementsGeneral Notation 1: Brownian Motions and Stochastic Integrals 1.1 INTRODUCTION1.2 BASIC NOTATIONS OF PROBABILITY THEORY1.3 STOCHASTIC PROCESSES1.4 BROWNIAN MOTIONS1.5 STOCHASTIC INTEGRALS1.6 ITO'S FORMULA1.7 MOMENT INEQUALITIES1.8 GRONWALL-TYPE INEQUALITIES2: Stochastic Differential Equations 2.1 INTRODUCTION2.2 STOCHASTIC DIFFERENTIAL EQUATIONS2.3 EXISTENCE AND UNIQUENESS OF SOLUTIONS2.4 LP-ESTIMATES2.5 ALMOST SURELY ASYMPTOTIC ESTIMATES2.6 CARATHEODORY'S APPROXIMATE SOLUTIONS2.7 EULER-MARUYAMA'S APPROXIMATE SOLUTIONS2.8 SDE AND PDE: FEYNMAN-KAC'S FORMULA2.9 THE SOLUTIONS AS MARKOV PROCESSES3: Linear Stochastic Differential Equations 3.1 INTRODUCTION3.2 STOCHASTIC LIOUVILLE'S FORMULA3.3 THE VARIATION-OF-CONSTANTS FORMULA3.4 CASE STUDIES3.5 EXAMPLES4: Stability of Stochastic Differential Equations 4.1 INTRODUCTION4.2 STABILITY IN PROBABILITY4.3 ALMOST SURE EXPONENTIAL STABILITY4.4 MOMENT EXPONENTIAL STABILITY4.5 STOCHASTIC STABILIZATION AND DESTABILIZATION4.6 FURTHER TOPICS5: Stochastic Functional Differential Equations 5.1 INTRODUCTION5.2 EXISTENCE-AND-UNIQUENESS THEOREMS5.3 STOCHASTIC DIFFERENTIAL DELAY EQUATIONS5.4 EXPONENTIAL ESTIMATES5.5 APPROXIMATE SOLUTIONS5.6 STABILITY THEORY-RAZUMIKHIN THEOREMS5.7 STOCHASTIC SELF-STABILIZATION6: Stochastic Equations of Neutral Type 6.1 INTRODUCTION6.2 NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS6.3 NEUTRAL STOCHASTIC DIFFERENTIAL DELAY EQUATIONS6.4 MOMENT AND PATHWISE ESTIMATES6.5 Lp-CONTINUITY6.6 EXPONENTIAL STABILITY7: Backward Stochastic Differential Equations 7.1 INTRODUCTION7.2 MARTINGALE REPRESENTATION THEOREM7.3 EQUATIONS WITH LIPSCHITZ COEFFICIENTS7.4 EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS7.5 REGULARITIES7.6 BSDE AND QUASILINEAR PDE8: Stochastic Oscillators 8.1 INTRODUCTION8.2 THE CAMERON-MARTIN-GIRSANOV THEOREM8.3 NONLINEAR STOCHASTIC OSCILLATORS8.4 LINEAR STOCHASTIC OSCILLATORS8.5 ENERGY BOUNDS9: Applications to Economics and Finance 9.1 INTRODUCTION9.2 STOCHASTIC MODELLING IN ASSET PRICES9.3 OPTIONS AND THEIR VALUES9.4 OPTIMAL STOPPING PROBLEMS9.5 STOCHASTIC GAMES10: Stochastic Neural Networks 10.1 INTRODUCTION10.2 STOCHASTIC NEURAL NETWORKS10.3 STOCHASTIC NEURAL NETWORKS WITH DELAYS11: Stochastic Delay Population Systems 11.1 INTRODUCTION11.2 NOISE INDEPENDENT OP POPULATION SIZES11.3 NOISE DEPENDENT ON POPULATION SIZES: PART I11.4 NOISE DEPENDENT ON POPULATION SIZES: PART II11.5 STOCHASTIC DELAY LOTKA-VOLTERRA FOOD CHAINBibliographical NotesReferencesIndex

Reviews

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

<p><p> ... 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. <br> --Professor G.G. Yin, Wayne State University, USA<p><p>Praise for the first edition: <br> 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. <br> --Professor Martynuk, Ukraine Academy of Sciences

Author Information

Xuerong Mao, Strathclyde University, UK

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