1. Preliminaries. A. Set Theory and General Topology. B. Probability Theory. C. Random Processes. D. Wiener-Levy Calculus -- 2. Computation of Expectations in Finite Dimension. A. Mathematical Framework of Simulation. B. The Monte Carlo Method. C. Low-Discrepancy Sequences. D. Numerical Computation of Conditional Expectation -- 3. Simulation of Random Processes. A. Integration in Large or Infinite Dimensions. B. Representations of Stationary Fields. C. Markov Processes. D. Processes with Stationary Independent Increments. E. Point Processes -- 4. Deterministic Resolution of Some Markovian Problems. A. Elements in Markovian Potential Theory. B. Balayage Algorithms. C. Reduced Function Algorithm. D. The Carre du Champ Operator -- 5. Stochastic Differential Equations and Brownian Functionals. A. Lipschitzian Stochastic Differential Equations: Ito's Theorem. B. Discretization of SDEs. C. Irregularity of Brownian Functionals. D. Simulatable Functionals
E. Symbolic Expansions of Solutions to SDEs. F. Application of the Shift Method to Multiple Wiener Integrals and to Solutions of SDEs
Analysis
Probabilities
Stochastic processes
Probabilities
Notes
"A Wiley-Interscience publication."
Bibliography
Includes bibliographical references (pages 337-351) and index
