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Limit theorems of probability theory / Yu. V. Prokhorov

Public ISBD Titre : Limit theorems of probability theory Type de document : texte imprimé Auteurs : Yu. V. Prokhorov, Auteur ; V. Statulevicius, Auteur Editeur : New York : Springer-Verlag Année de publication : 2000 Importance : 273 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-57045-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Mots-clés : Limit theorems,Markov chain,Normal distribution,Probability theory,Random variable,large deviations Index. décimale : 04-05 Probabilité et statistique Résumé : This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con­ fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics. Note de contenu : Contents I Classical-Type Limit Theorems for Sums of Independent Random Variables II The Accuracy of Gaussian Approximation in Banach Spaces III Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution IV Refinements of the Central Limit Theorem for Homogeneous Markov Chains V Limit Theorems on Large Deviations Limit theorems of probability theory [texte imprimé] / Yu. V. Prokhorov, Auteur ; V. Statulevicius, Auteur . - New York : Springer-Verlag, 2000 . - 273 p. : couv. ill. en coul. ; 24 cm. ISSN : 978-3-540-57045-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Mots-clés : Limit theorems,Markov chain,Normal distribution,Probability theory,Random variable,large deviations Index. décimale : 04-05 Probabilité et statistique Résumé : This book consists of five parts written by different authors devoted to various problems dealing with probability limit theorems. The first part, "Classical-Type Limit Theorems for Sums ofIndependent Random Variables" (V.v. Petrov), presents a number of classical limit theorems for sums of independent random variables as well as newer related results. The presentation dwells on three basic topics: the central limit theorem, laws of large numbers and the law of the iterated logarithm for sequences of real-valued random variables. The second part, "The Accuracy of Gaussian Approximation in Banach Spaces" (V. Bentkus, F. G6tze, V. Paulauskas and A. Rackauskas), reviews various results and methods used to estimate the convergence rate in the central limit theorem and to construct asymptotic expansions in infinite-dimensional spaces. The authors con­ fine themselves to independent and identically distributed random variables. They do not strive to be exhaustive or to obtain the most general results; their aim is merely to point out the differences from the finite-dimensional case and to explain certain new phenomena related to the more complex structure of Banach spaces. Also reflected here is the growing tendency in recent years to apply results obtained for Banach spaces to asymptotic problems of statistics. Note de contenu : Contents I Classical-Type Limit Theorems for Sums of Independent Random Variables II The Accuracy of Gaussian Approximation in Banach Spaces III Approximation of Distributions of Sums of Weakly Dependent Random Variables by the Normal Distribution IV Refinements of the Central Limit Theorem for Homogeneous Markov Chains V Limit Theorems on Large Deviations

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Probability theory Vol. III / Yu. V. Prokhorov

Public ISBD Titre : Probability theory Vol. III : stochastic calculus Type de document : texte imprimé Auteurs : Yu. V. Prokhorov, Auteur ; A. N. Shiryaev, Auteur ; P. B. Slater, Traducteur Editeur : New York : Springer-Verlag Année de publication : 1998 Collection : Encyclopaedia of Mathematical Sciences Importance : 253 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-54687-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are well-known experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods. Note de contenu : Contents Chapter 1 Introduction to Stochastic Calculus Chapter 2 Stochastic Differential and Evolution Equations I Stochastic Differential Equations (SDEs) II Stochastic Evolution Equations III Stochastic Calculus (Malliavin Calculus). Applications to Stochastic Differential Equations Chapter 3 Stochastic Calculus on Filtered Probability Spaces I Elements of the General Theory of Stochastic Processes II Semimartingales. Stochastic Integrals III Absolute Continuity and Singularity of Probability Distributions Chapter 4 Martingales and Limit Theorems for Stochastic Processes I Theory: Weak Convergence of Probability Measures on Metric Spaces II Applications: The Invariance Principle and Diffusion Approximation Author Index Subject Index Probability theory Vol. III : stochastic calculus [texte imprimé] / Yu. V. Prokhorov, Auteur ; A. N. Shiryaev, Auteur ; P. B. Slater, Traducteur . - New York : Springer-Verlag, 1998 . - 253 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISSN : 978-3-540-54687-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are well-known experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods. Note de contenu : Contents Chapter 1 Introduction to Stochastic Calculus Chapter 2 Stochastic Differential and Evolution Equations I Stochastic Differential Equations (SDEs) II Stochastic Evolution Equations III Stochastic Calculus (Malliavin Calculus). Applications to Stochastic Differential Equations Chapter 3 Stochastic Calculus on Filtered Probability Spaces I Elements of the General Theory of Stochastic Processes II Semimartingales. Stochastic Integrals III Absolute Continuity and Singularity of Probability Distributions Chapter 4 Martingales and Limit Theorems for Stochastic Processes I Theory: Weak Convergence of Probability Measures on Metric Spaces II Applications: The Invariance Principle and Diffusion Approximation Author Index Subject Index

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Code-barres	Cote	Support	Localisation	Section	Disponibilité	N.Inventaire
500	04-05-04	Livre	Bibliothèque de Génie Electrique- USTO	Documentaires	Exclu du prêt	500