Stochastic Simulation and Monte Carlo Methods Mathematical Foundations of Stochastic Simulation /

• Main Authors: Graham, Carl (Author), Talay, Denis (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Stochastic Modelling and Applied Probability, 68
• Subjects: Mathematics.; Economics, Mathematical.; Numerical analysis.; Probabilities.; Probability Theory and Stochastic Processes.; Numerical Analysis.; Quantitative Finance.

In various scientific and industrial fields, stochastic simulations are taking on a new importance. This is due to the increasing power of computers and practitioners’ aim to simulate more and more complex systems, and thus use random parameters as well as random noises to model the parametric uncer...

Table of Contents:

• Part I:Principles of Monte Carlo Methods
• 1.Introduction
• 2.Strong Law of Large Numbers and Monte Carlo Methods
• 3.Non Asymptotic Error Estimates for Monte Carlo Methods
• Part II:Exact and Approximate Simulation of Markov Processes
• 4.Poisson Processes
• 5.Discrete-Space Markov Processes
• 6.Continuous-Space Markov Processes with Jumps
• 7.Discretization of Stochastic Differential Equations
• Part III:Variance Reduction, Girsanov’s Theorem, and Stochastic Algorithms
• 8.Variance Reduction and Stochastic Differential Equations
• 9.Stochastic Algorithms
• References
• Index.