Author | Kloeden, Peter E. author |
---|---|
Title | Numerical Solution of SDE Through Computer Experiments [electronic resource] / by Peter E. Kloeden, Eckhard Platen, Henri Schurz |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994 |
Connect to | http://dx.doi.org/10.1007/978-3-642-57913-4 |
Descript | XIV, 294 p. online resource |
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