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Tuesday, July 28, 2020 | History

1 edition of Numerical Solution of Stochastic Differential Equations found in the catalog.

Numerical Solution of Stochastic Differential Equations

by Peter E. Kloeden

  • 382 Want to read
  • 12 Currently reading

Published by Springer Berlin Heidelberg in Berlin, Heidelberg .
Written in English

    Subjects:
  • Global analysis (Mathematics),
  • Numerical analysis,
  • Statistics,
  • Engineering mathematics,
  • Mathematics,
  • Distribution (Probability theory),
  • Economics

  • About the Edition

    The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary. The book is also accessible to others who only require numerical recipes. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included.

    Edition Notes

    Statementby Peter E. Kloeden, Eckhard Platen
    SeriesApplications of Mathematics, Stochastic Modelling and Applied Probability -- 23, Applications of Mathematics, Stochastic Modelling and Applied Probability -- 23
    ContributionsPlaten, Eckhard
    Classifications
    LC ClassificationsQA273.A1-274.9, QA274-274.9
    The Physical Object
    Format[electronic resource] /
    Pagination1 online resource (xxxvi, 636 p.)
    Number of Pages636
    ID Numbers
    Open LibraryOL27078040M
    ISBN 10364208107X, 3662126168
    ISBN 109783642081071, 9783662126165
    OCLC/WorldCa851370005

    Solutions of linear time-invariant differential equations 3 which is a very useful class of differential equations often arising in applications. The usefulness of linear equations is that we can actually solve these equationsFile Size: 1MB. The authors of treated the numerical solution of stochastic initial value problems based on a sample treatment of the right-hand side of the differential equations. The sample treatment approach developed in [6] has the advantage that conclusions remain true in the deterministic case, but in many situations the hypothesis assumed in [6] is not Cited by:

    The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, Read more. This book deals with numerical analysis of systems of both ordinary and stochastic differential equations. The first chapter is devoted to numerical solution problems of the Cauchy problem for stiff ordinary differential equation (ODE) systems by Rosenbrock-type methods (RTMs). Here, general solutions of consistency equations are obtained, which lead to the .

    Numerical solutions. Numerical solution of stochastic differential equations and especially stochastic partial differential equations is a young field relatively speaking. Almost all algorithms that are used for the solution of ordinary differential equations will work very poorly for SDEs, having very poor numerical convergence. This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems.


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Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden Download PDF EPUB FB2

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus.

This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such by: The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations ().

The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations Cited by: The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus.

This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations ().5/5(2).

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Stochastic Modelling and Applied Probability Book 64) - Kindle edition by Platen, Eckhard, Nicola Bruti-Liberati.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Numerical Solution of Stochastic Differential Equations 5/5(2). Author of books on numerical methods for stochastic differential equations and recent book on benchmark approach at Springer Verlag.

Has written more than papers in finance, insurance and applied mathematics and serves on the editorial boards of five international journals including Mathematical Finance and Quantitative Finance.

Numerical Solution of Stochastic Differential Equations. The aim of this book is to provide an accessible introduction to stochastic differ ential equations and their applications together with a systematic presentation of methods available for their numerical solution.5/5(3).

This book deals with numerical analysis of systems of both ordinary and stochastic differential equations. The first chapter is devoted to numerical solution problems of the Cauchy problem for stiff ordinary differential equation (ODE) systems by Rosenbrock-type methods (RTMs).Cited by: The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus.

This book provides an introduction to stochastic calculus and stochastic differential equations, in. In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of.

Numerical Solution of Stochastic Differential Equations. The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations.

This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations/5. Numerical solution of stochastic differential equations Peter E. Kloeden, Eckhard Platen The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus.

A new simple form of the Runge-Kutta method is derived. Keywords-Stochastic differential equation, Numerical solution, Monte Carlo method, RungeKutta method. INTRODUCTION We consider a linear Ito stochastic differential equation (SDE) with constant coefficients dXt = AXt dt + B dWt, for 0 Cited by: 7.

respectively, the numerical and the exact solution of the stochastic differential equation at time t„. In the present paper we adopt an L2-norm analysis because it can best exhibit the nonanticipating property [1] of the solutions of stochastic differential equations.

Our main results are a second-order scheme for scalar. The solutions of SDEs are of a different character compared with the solutions of classical ordinary and partial differential equations in the sense that the solutions of SDEs are stochastic processes. Thus it is a nontrivial matter to measure the efficiency of a given algorithm for finding numerical : Geon Ho Choe.

Summary This chapter contains sections titled: Memories of approximations of ordinary differential equations Euler approximation Higher‐order strong approximations First‐order weak approximations H.

Download numerical solution of stochastic differential equations or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get numerical solution of stochastic differential equations book now.

This site is like a library, Use search box in the widget to get ebook that you want. Numerical Solution Of. Request PDF | The Numerical Solution of Stochastic Differential Equations | 1. Probability and Statistics.- 2.

Probability and Stochastic Processes.- 3. Ito Stochastic Calculus.- 4. Stochastic. The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations.

This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the Brand: Springer Berlin Heidelberg. This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation.

The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential : Springer International Publishing. The differential equations we consider in most of the book are of the form Y′(t) = f(t,Y(t)), where Y(t) is an unknown function that is being sought.

The given function f(t,y) of two variables defines the differential equation, and exam ples are given in Chapter 1. This equation is called a first-order differential equation because it File Size: 1MB.The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations.

This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations.This book provides a unified treatment of both regular (or random) and Ito stochastic differential equations.

It focuses on solution methods, including some developed only recently. Applications are discussed, in particular an insight is given into both the mathematical structure, and the most efficient solution methods (analytical as well as.