Numerical Solution of SDE Through Computer Experiments: Universitext
Autor Peter Eris Kloeden, Eckhard Platen, Henri Schurzen Limba Engleză Paperback – 20 dec 1993
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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
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
GraduateCuprins
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.
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