Stochastic simulation and Monte Carlo methods : mathematical foundations of stochastic simulation
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 uncert...
保存先:
| 主要な著者: | , |
|---|---|
| フォーマット: | Livre numérique |
| 言語: | Anglais |
| 出版事項: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| 版: | 1st ed. 2013. |
| シリーズ: | Stochastic Modelling and Applied Probability
68 |
| 主題: | |
| オンライン･アクセス: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| 注記: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Stochastic simulation and Monte Carlo methods, mathematical foundations of stochastic simulation, Carl Graham, Denis Talay, 2013, Berlin, Springer-Verlag, 1 vol. (XVI-260 p.), Stochastic modelling and applied probability, 978-3-642-39362-4 • Stochastic Simulation and Monte Carlo Methods, Texte imprimé, 9783642393648 |
目次:
- Part I Principles of Monte Carlo Methods
- Part II Exact and Approximate Simulation of Markov Processes
- Part III Variance Reduction, Girsanov s Theorem, and Stochastic Algorithms
- 1 Introduction
- 2 Strong Law of Large Numbers and Monte Carlo Methods
- 3 Non-asymptotic Error Estimates for Monte Carlo Methods
- 4 Poisson Processes as Particular Markov Processes
- 5 Discrete-Space Markov Processes
- 6 Continuous-Space Markov Processes with Jumps
- 7 Discretization of Stochastic Differential Equations
- 8 Variance Reduction and Stochastic Differential Equations
- 9 Stochastic Algorithms
- 1.1 Why Use Probabilistic Models and Simulations?
- 1.2 Organization of the Monograph
- 2.1 Strong Law of Large Numbers, Examples of Monte Carlo Methods
- 2.2 Simulation Algorithms for Simple Probability Distributions
- 2.3 Discrete-Time Martingales, Proof of the SLLN
- 2.4 Problems
- 3.1 Convergence in Law and Characteristic Functions
- 3.2 Central Limit Theorem
- 3.3 Berry Esseen s Theorem
- 3.4 Bikelis Theorem
- 3.5 Concentration Inequalities
- 3.6 Elementary Variance Reduction Techniques
- 3.7 Problems
- 4.1 Quick Introduction to Markov Processes
- 4.2 Poisson Processes: Characterization, Properties
- 4.3 Simulation and Approximation
- 4.4 Problems
- 5.1 Characterization, Specification, Properties
- 5.2 Constructions, Existence, Simulation, Equations
- 5.3 Problems
- 6.1 Preliminaries
- 6.2 Markov Processes Evolving Only by Isolated Jumps
- 6.3 Markov Processes Following an Ordinary Differential Equation
- 6.4 Problems
- 7.1 Reminders on Itô s Stochastic Calculus
- 7.2 Euler and Milstein Schemes
- 7.3 Moments of the Solution and of Its Approximations
- 7.4 Convergence Rates in Lp( ) Norm and Almost Surely
- 7.5 Monte Carlo Methods for Parabolic Partial Differential Equations
- 7.6 Optimal Convergence Rate: The Talay Tubaro Expansion
- 7.7 Romberg Richardson Extrapolation Methods
- 7.8 Probabilistic Interpretation and Estimates for Parabolic Partial Differential Equations
- 8.1 Preliminary Reminders on the Girsanov Theorem
- 8.2 Control Variates Method
- 8.3 Variance Reduction for Sensitivity Analysis
- 8.4 Importance Sampling Method
- 8.5 Statistical Romberg Method
- 8.6 Problems
- 9.1 Introduction