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Effective dynamics of stochastic partial differential equations / Jinqiao Duan / Amsterdam ; New York ; Londres ; Rio de Janeiro : Elsevier (2014)
Titre : Effective dynamics of stochastic partial differential equations Type de document : document électronique Auteurs : Jinqiao Duan ; Wei [Nanjing - CHN] Wang Editeur : Amsterdam ; New York ; Londres ; Rio de Janeiro : Elsevier Année de publication : 2014 Collection : Elsevier insights Importance : 282 p. Format : 1 online resource ISBN/ISSN/EAN : 978-0-12-801269-7 Langues : Anglais (eng) Tags : Stochastic partial differential equations Probability Statistics Stochastics partial differential equations Résumé : Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty. Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Solutions or hints to all Exercises Note de contenu : Hardcover ISBN: 9780128008829 En ligne : https://www.elsevier.com/books/effective-dynamics-of-stochastic-partial-differen [...] Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=139793 Effective dynamics of stochastic partial differential equations [document électronique] / Jinqiao Duan ; Wei [Nanjing - CHN] Wang . - Amsterdam ; New York ; Londres ; Rio de Janeiro : Elsevier, 2014 . - 282 p. ; 1 online resource. - (Elsevier insights) .
ISBN : 978-0-12-801269-7
Langues : Anglais (eng)
Tags : Stochastic partial differential equations Probability Statistics Stochastics partial differential equations Résumé : Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty. Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Solutions or hints to all Exercises Note de contenu : Hardcover ISBN: 9780128008829 En ligne : https://www.elsevier.com/books/effective-dynamics-of-stochastic-partial-differen [...] Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=139793 Large deviations for stochastic nonlinear Schrödinger equations and applications / Eric Gautier / Malakoff : ENSAE (2005)
Titre : Large deviations for stochastic nonlinear Schrödinger equations and applications Type de document : document électronique Auteurs : Eric Gautier Editeur : Malakoff : ENSAE Année de publication : 2005 Autre Editeur : Rennes : Université Rennes 1 Importance : application/pdf Langues : Français (fre) Descripteurs : Publication d'auteur CREST , Publication d'auteur ENSAE , Théorèmes limites , Thèse ENSAE Tags : Nonlinear Schrödinger equation Large deviations Stochastic partial differential equations Solitary waves Blow-up fractional Brownian motion Support theorems Equations de Schrödinger non linéaires Grandes déviations équations aux dérivées partielles stochastiques Ondes solitaires Explosion en temps fini mouvement Brownien fractionnaire Théorèmes de support Résumé : This thesis is dedicated to the study of the small noise asymptotic in random perturbations of nonlinear Schrödinger equations. The noises are Gaussian, mostly white in time and always colored in space, of additive and multiplicative types. Large deviations are such that the behavior of the stochastic system differs significantly from the deterministic one. As the noise goes to zero the probability of such rare events goes to zero on a logarithmic scale with speed given by the noise amplitude. We prove large deviation principles at the level of paths. The rate of convergence to zero of the logarithm of the probabilities is related to an optimal control problem. Our first application is to the blow-up times. We then apply our results to the study of the small noise asymptotic of the tails of the mass and position of the soliton-like pulse in a "white noise limit". The fluctuations of these quantities are the main causes of error in optical soliton transmission. We also consider the problem of the mean exit times and the exit points from a neighborhood of zero for weakly damped equations. Finally we present large deviations and a support theorem for fractional additive Gaussian noises Note de thèse : Th. doct. : math. appliq. : Rennes 1 : 2005 En ligne : http://pastel.paristech.org/1527/ Format de la ressource électronique : application/pdf Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=79618 Large deviations for stochastic nonlinear Schrödinger equations and applications [document électronique] / Eric Gautier . - Malakoff : ENSAE : Rennes : Université Rennes 1, 2005 . - application/pdf.
Langues : Français (fre)
Descripteurs : Publication d'auteur CREST , Publication d'auteur ENSAE , Théorèmes limites , Thèse ENSAE Tags : Nonlinear Schrödinger equation Large deviations Stochastic partial differential equations Solitary waves Blow-up fractional Brownian motion Support theorems Equations de Schrödinger non linéaires Grandes déviations équations aux dérivées partielles stochastiques Ondes solitaires Explosion en temps fini mouvement Brownien fractionnaire Théorèmes de support Résumé : This thesis is dedicated to the study of the small noise asymptotic in random perturbations of nonlinear Schrödinger equations. The noises are Gaussian, mostly white in time and always colored in space, of additive and multiplicative types. Large deviations are such that the behavior of the stochastic system differs significantly from the deterministic one. As the noise goes to zero the probability of such rare events goes to zero on a logarithmic scale with speed given by the noise amplitude. We prove large deviation principles at the level of paths. The rate of convergence to zero of the logarithm of the probabilities is related to an optimal control problem. Our first application is to the blow-up times. We then apply our results to the study of the small noise asymptotic of the tails of the mass and position of the soliton-like pulse in a "white noise limit". The fluctuations of these quantities are the main causes of error in optical soliton transmission. We also consider the problem of the mean exit times and the exit points from a neighborhood of zero for weakly damped equations. Finally we present large deviations and a support theorem for fractional additive Gaussian noises Note de thèse : Th. doct. : math. appliq. : Rennes 1 : 2005 En ligne : http://pastel.paristech.org/1527/ Format de la ressource électronique : application/pdf Permalink : https://genes.bibli.fr/index.php?lvl=notice_display&id=79618 Documents numériques
Large deviations for stochastic nonlinear Schrödinger equations and applicationsURL