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Viser: Numerical Solution of SDE Through Computer Experiments
Numerical Solution of SDE Through Computer Experiments
Peter E. Kloeden, Eckhard Platen og Henri Schurz
(1993)
Sprog: Engelsk
Springer Berlin / Heidelberg
710,00 kr.
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Detaljer om varen
- 1. Udgave
- Paperback: 292 sider
- Udgiver: Springer Berlin / Heidelberg (December 1993)
- Forfattere: Peter E. Kloeden, Eckhard Platen og Henri Schurz
- ISBN: 9783540570745
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.
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.
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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Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927