Numerical Solution of SDE Through Computer Experiments

Peter Eris Kloeden, Henri Schurz, Eckhard Platen

ISBN 10: 3540570748 / ISBN 13: 9783540570745

Editore: Springer Berlin Heidelberg, 2002

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Zustand: Gut - Gebrauchs- und Lagerspuren. 1. Auflage. Außen: verschmutzt, vergilbt. Innen: Seiten vergilbt. Aus der Auflösung einer renommierten Bibliothek. Kann Stempel beinhalten. | Seiten: 312 | Sprache: Englisch | Produktart: Bücher. Codice articolo 16477/203

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Titolo: Numerical Solution of SDE Through Computer ...

Casa editrice: Springer Berlin Heidelberg

Data di pubblicazione: 2002

Legatura: Brossura

Condizione: Gut

Edizione: terza edizione

Descrizione articolo

Riassunto:

This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations. It also creates an intuitive understanding of the necessary theoretical background. Software containing programs for over 100 problems is available online.

Contenuti:

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.