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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