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Numerical Solution of SDE Through Computer Experiments

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...

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Bibliographic Details
Main Authors: Kloeden, Peter Eris, Platen, Eckhard (Author), Schurz, Henri (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1994, 1994
Edition:1st ed. 1994
Series:Universitext
Subjects:
Mathematical Analysis
Analysis
Numerical Analysis
Analysis (mathematics)
Probability Theory And Stochastic Processes
Probabilities
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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

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