Numerical Integration of Stochastic Differential Equations

By: G.N. Milstein

Write A Review

Hardcover | 30 November 1994

At a Glance

Hardcover
184 Pages

Dimensions(cm)
25.4 x 17.15 x 1.91

Hardcover

$229.75

or 4 interest-free payments of $57.44 with

Ships in 7 to 10 business days

This text is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book should be of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Calculus & Mathematical Analysis Numerical Analysis Differential Calculus & Equations Probability & Statistics Number Theory Computing & I.T.Computer Science Mathematical Theory of Computation

Computer Programming & Software Development Algorithms & Data Structures

Introduction	p. 1
Mean-square approximation of solutions of systems of stochastic differential equations	p. 11
Theorem on the order of convergence (theorem on the relation between approximation on a finite interval and one-step approximation)	p. 11
Methods based on an analog of Taylor expansion of the solution	p. 23
Explicit and implicit methods of order 3/2 for systems with additive noises	p. 37
Optimal integration methods for linear systems with additive noises	p. 56
A strengthening of the main convergence theorem	p. 63
Modeling of Ito integrals	p. 75
Modeling Ito integrals depending on a single noise	p. 75
Modeling Ito integrals depending on several noises	p. 90
Weak approximation of solutions of systems of stochastic differential equations	p. 101
One-step approximation	p. 101
The main theorem on convergence of weak approximations and methods of order of accuracy two	p. 112
A method of order of accuracy three for systems with additive noises	p. 118
An implicit method	p. 127
Reducing the error of the Monte-Carlo method	p. 130
Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals	p. 135
Methods of order of accuracy two for computing Wiener integrals of functionals of integral type	p. 135
Methods of order of accuracy four for computing Wiener integrals of functionals of exponential type	p. 145
Bibliography	p. 165
Index	p. 169
Table of Contents provided by Blackwell. All Rights Reserved.

Numerical Integration of Stochastic Differential Equations

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Computer Science

Genesis

Artificial Intelligence, Hope, and the Human Spirit

Nexus

A Brief History of Information Networks from the Stone Age to AI

If Anyone Builds It, Everyone Dies

The Case Against Superintelligent AI

Autonomous

Why the Fittest Businesses Embrace AI-First Strategies and Digital Labor

The New Age of Sexism

How the AI Revolution is Reinventing Misogyny

As If Human

Ethics and Artificial Intelligence

Creative Machines

AI, Art & Us

Windows 11 For Seniors For Dummies, 2nd Edition

For Dummies (Computer/Tech)

The AI Con

How To Fight Big Tech's Hype and Create the Future We Want

Empire of AI

Inside the reckless race for total domination

Dr. Bot

Why Human Doctors Fail Us and How AI Can Save Lives

Windows 11 For Dummies, 2nd Edition

Windows 11 For Dummies

AI Engineering

Building Applications with Foundation Models

The Coming Wave

AI, Power and Our Future

Rapid Transformation

Shape the Future Now with Ancient Ritual, Awakened Thinking and Emerging Technology

Machine Learning in Protein Science

Efficient Prediction of Protein Structures and Properties

BIM and Construction Health and Safety

1st Edition - Uncovering, Adoption and Implementation

Data-driven BIM for Energy Efficient Building Design

1st Edition

Effective Modern C++

42 Specific Ways to Improve Your Use of C++11 And C++14

Co-Intelligence

Living and Working with AI

Scary Smart

The Future of Artificial Intelligence and How You Can Save Our World

Spring Boot Microservices

Design, Implementation and Deployment

The Shortest History of Ai

The Six Essential Ideas That Animate It

Geometric Science of Information

7th International Conference, GSI 2025, Saint-Malo, France, October 29¢"31, 2025, Proceedings, Part III

This product is categorised by