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Numerical Solution of SDE Through Computer Experiments: Universitext

Autor Peter Eris Kloeden, Eckhard Platen, Henri Schurz
en Limba Engleză Paperback – 20 dec 1993
The numerical solution of stochastic differential equations is becoming an in­ dispensible worktool in a multitude of disciplines, bridging a long-standing gap between the well advanced theory of stochastic differential equations and its application to specific examples. This has been made possible by the much greater accessibility to high-powered computers at low-cost combined with the availability of new, effective higher order numerical schemes for stochastic dif­ ferential equations. Many hitherto intractable problems can now be tackled successfully and more realistic modelling with stochastic differential equations undertaken. The aim of this book is to provide a computationally oriented introduction to the numerical solution of stochastic differential equations, using computer experiments to develop in the readers an ability to undertake numerical studies of stochastic differential equations that arise in their own disciplines and an understanding, intuitive at least, of the necessary theoretical background. It is related to, but can also be used independently of the monograph P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Applications of Mathematics Series Vol. 23, Springer-Verlag, Hei­ delberg, 1992, which is more theoretical, presenting a systematic treatment of time-discretized numerical schemes for stochastic differential equations along with background material on probability and stochastic calculus. To facilitate the parallel use of both books, the presentation of material in this book follows that in the monograph closely.
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Specificații

ISBN-13: 9783540570745
ISBN-10: 3540570748
Pagini: 312
Ilustrații: XIV, 294 p.
Dimensiuni: 155 x 235 x 16 mm
Greutate: 0.47 kg
Ediția:1994
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Universitext

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Graduate

Cuprins

1: Background on Probability and Statistics.- 1.1 Probability and Distributions.- 1.2 Random Number Generators.- 1.3 Moments and Conditional Expectations.- 1.4 Random Sequences.- 1.5 Testing Random Numbers.- 1.6 Markov Chains as Basic Stochastic Processes.- 1.7 Wiener Processes.- 2: Stochastic Differential Equations.- 2.1 Stochastic Integration.- 2.2 Stochastic Differential Equations.- 2.3 Stochastic Taylor Expansions.- 3: Introduction to Discrete Time Approximation.- 3.1 Numerical Methods for Ordinary Differential Equations.- 3.2 A Stochastic Discrete Time Simulation.- 3.3 Pathwise Approximation and Strong Convergence.- 3.4 Approximation of Moments and Weak Convergence.- 3.5 Numerical Stability.- 4: Strong Approximations.- 4.1 Strong Taylor Schemes.- 4.2 Explicit Strong Schemes.- 4.3 Implicit Strong Approximations.- 4.4 Simulation Studies.- 5: Weak Approximations.- 5.1 Weak Taylor Schemes.- 5.2 Explicit Weak Schemes and Extrapolation Methods.- 5.3 Implicit Weak Approximations.- 5.4 Simulation Studies.- 5.5 Variance Reducing Approximations.- 6: Applications.- 6.1 Visualization of Stochastic Dynamics.- 6.2 Testing Parametric Estimators.- 6.3 Filtering.- 6.4 Functional Integrals and Invariant Measures.- 6.5 Stochastic Stability and Bifurcation.- 6.6 Simulation in Finance.- References.- List of PC-Exercises.- Frequently Used Notations.

Textul de pe ultima copertă

This is a computer experimental introduction to the numerical solution of stochastic differential equations. A downloadable software software containing programs for over 100 problems is provided at one of the following homepages:
http://www.math.uni-frankfurt.de/numerik/kloeden/
http://www.business.uts.edu.au/finance/staff/eckard.html
http://www.math.siu.edu/schurz/SOFTWARE/
to enable the reader to develop an intuitive understanding of the issues involved. Applications include stochastic dynamical systems, filtering, parametric estimation and finance modeling.
The book is intended for readers without specialist stochastic background who want to apply such numerical methods to stochastic differential equations that arise in their own field. It can also be used as an introductory textbook for upper-level undergraduate or graduate students in engineering, physics and economics.

Caracteristici

Complements the authors' previous book for readers needing less theoretical background information Provides calculation models for concrete problems using SDE This 2nd volume can be used quite independently of the first Includes supplementary material: sn.pub/extras