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...
Bewaard in:
| Hoofdauteurs: | , |
|---|---|
| Formaat: | Livre numérique |
| Taal: | Anglais |
| Gepubliceerd in: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Editie: | 1st ed. 2013. |
| Reeks: | Stochastic Modelling and Applied Probability
68 |
| Onderwerpen: | |
| Online toegang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Opmerking: |
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 |
| LEADER | 06673nam a22004217a 4500 | ||
|---|---|---|---|
| 001 | 947075 | ||
| 008 | 131018q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN172428165 | ||
| 020 | |a 9783642393631 | ||
| 041 | 0 | |a eng | |
| 082 | |a 519.2 | ||
| 084 | |a 60H10. 2010 | ||
| 084 | |a 65C05. 2010 | ||
| 084 | |a 65R20. 2010 | ||
| 100 | 1 | |a Graham, Carl, |d 19..-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Stochastic simulation and Monte Carlo methods : |b mathematical foundations of stochastic simulation |c by Carl Graham, Denis Talay. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Stochastic Modelling and Applied Probability |v 68 |x 2197-439X | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 0 | |a 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 | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 uncertainties and the lack of knowledge on the physics of these systems. The error analysis of these computations is a highly complex mathematical undertaking. Approaching these issues, the authors present stochastic numerical methods and prove accurate convergence rate estimates in terms of their numerical parameters (number of simulations, time discretization steps). As a result, the book is a self-contained and rigorous study of the numerical methods within a theoretical framework. After briefly reviewing the basics, the authors first introduce fundamental notions in stochastic calculus and continuous-time martingale theory, then develop the analysis of pure-jump Markov processes, Poisson processes, and stochastic differential equations. In particular, they review the essential properties of Itô integrals and prove fundamental results on the probabilistic analysis of parabolic partial differential equations. These results in turn provide the basis for developing stochastic numerical methods, both from an algorithmic and theoretical point of view. The book combines advanced mathematical tools, theoretical analysis of stochastic numerical methods, and practical issues at a high level, so as to provide optimal results on the accuracy of Monte Carlo simulations of stochastic processes. It is intended for master and Ph.D. students in the field of stochastic processes and their numerical applications, as well as for physicists, biologists, economists and other professionals working with stochastic simulations, who will benefit from the ability to reliably estimate and control the accuracy of their simulations. | ||
| 650 | |a Processus stochastiques | ||
| 650 | |a Méthode de Monte-Carlo | ||
| 650 | |a Markov, processus de | ||
| 700 | 1 | |a Talay, Denis, |d 1955-...., |c auteur en mathématiques financières. |4 aut | |
| 776 | 0 | |0 172086868 |t Stochastic simulation and Monte Carlo methods |o mathematical foundations of stochastic simulation |f Carl Graham, Denis Talay |d 2013 |c Berlin |n Springer-Verlag |p 1 vol. (XVI-260 p.) |s Stochastic modelling and applied probability |z 978-3-642-39362-4 | |
| 776 | 0 | |t Stochastic Simulation and Monte Carlo Methods |b Texte imprimé |z 9783642393648 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-3-642-39363-1 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-G8CQ4FXR-H |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:747816824 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-3-642-39363-1 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:750833335 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-3-642-39363-1 |z Accès INSA CVL | |
| 997 | |0 947075 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||