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Numerical Solution of Stochastic Differential Equations (Hardback)

Numerical Solution of Stochastic Differential Equations (Hardback)

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LIKE NEW: This book is in excellent, like-new condition and was printed on acid-free paper.
NOTE: British spelling.

Product Details

From the back cover: "The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to the peculiarities of stochastic calculus."

This book "assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, through many chapters being with a descriptive summary. The book is also accessible to other who only require numerical recipes.

"The stochastic Taylor expansion provides the basis for discrete time numerical methods for stochastic differential equations. The book presents many new results on higher-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extrapolation 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 200 PC-exercises are included."

BRIEF CONTENTS

  • Suggestions for the Reader
  • Basic Notation
  • Brief Survey of Stochastic Numerical Methods
  • Part I. Preliminaries
    1. Probability and Statistics
    2. Probability and Stochastic Processes
  • Part II. Stochastic Differential Equations
    1. Ito Stochastic Calculus
    2. Stochastic Differential Equations
    3. Stochastic Taylor Expansions
  • Part III. Applications of Stochastic Differential Equations
    1. Modelling with Stochastic Differential Equations
    2. Applications of Stochastic Differential Equations
  • Part IV. Time Discrete Approximations
    1. Time Discrete Approximation of Deterministic Differential Equations
    2. Introduction to Stochastic Time Discrete Approximation
  • Part V. Strong Approximations
    1. Strong Taylor Approximations
    2. Explicit Strong Approximations
    3. Implicit Strong Approximations
    4. Selected Applications of Strong Approximations
  • Part VI. Weak Approximations
    1. Weak Taylor Approximations
    2. Explicit and Implicit Weak Approximations
    3. Variance Reduction Methods
    4. Selected Applications of Weak Approximations
  • Solutions of Exercises
  • Bibliographical Notes
  • Bibliography
  • Index
View full details

AUTHOR: Kloeden;Peter E. and Eckhard Platen
PUBLISHER: Springer
ISBN-13: 9783540540625
ISBN-10: 3540540628
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