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...
محفوظ في:
| المؤلفون الرئيسيون: | , |
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| التنسيق: | Livre numérique |
| اللغة: | Anglais |
| منشور في: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| الطبعة: | 1st ed. 2013. |
| سلاسل: | Stochastic Modelling and Applied Probability
68 |
| الموضوعات: | |
| الوصول للمادة أونلاين: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| ملاحظة: |
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 |
| الملخص: | 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. |
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| وصف المادة: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ردمك: | 9783642393631 |
| تدمد: | 2197-439X |
| وصول: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |