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A modern introduction to probability and statistics / F. M. Dekking

Public ISBD Titre : A modern introduction to probability and statistics : understanding why and how Type de document : texte imprimé Auteurs : F. M. Dekking, Auteur ; C. Kraaikamp, Auteur ; H. P. Lopuhaa, Auteur Editeur : New York : Springer-Verlag Année de publication : 2005 Collection : Springer Texts in Statistics Importance : 487 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-1-85233-896-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap. This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects. Note de contenu : Contents 1 Why Probability and Statistics? 2 Outcomes, Events and Probability 3 Conditional Probability and Independence 4 Discrete Random Variables 5 Continuous Random Variables 6 Simulation 7 Expectation and Variance 8 Computations with Random Variables 9 Joint Distributions and Independence 10 Covariance and Correlation 11 More Computations with More Random Variables 12 The Poisson Process 13 The Law of Large Numbers 14 The Central Limit Theorem 15 Exploratory Data Analysis: Graphical Summaries 16 Exploratory Data Analysis: Numerical Summaries 17 Basic Statistical Models 18 The Bootstrap 19 Unbiased Estimators 20 Efficiency and Mean Squared Error 21 Maximum Likelihood 22 The Method of Least Squares 23 Confidence Intervals for the Mean 24 More on Confidence Intervals 25 Testing Hypotheses: Essentials 26 Testing Hypotheses: Elaboration 27 The t-test 28 Comparing Two Samples A: Summary of distributions B: Tables of the normal and t-distributions C: Answers to selected exercices D: Full solutions to selected exercises -Index A modern introduction to probability and statistics : understanding why and how [texte imprimé] / F. M. Dekking, Auteur ; C. Kraaikamp, Auteur ; H. P. Lopuhaa, Auteur . - New York : Springer-Verlag, 2005 . - 487 p. : couv. ill. en coul. ; 24 cm.. - (Springer Texts in Statistics) . ISSN : 978-1-85233-896-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : Probability and Statistics are studied by most science students, usually as a second- or third-year course. Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real-life and using real data, the authors can show how the fundamentals of probabilistic and statistical theories arise intuitively. It provides a tried and tested, self-contained course, that can also be used for self-study. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to the students. In addition the book contains over 350 exercises, half of which have answers, of which half have full solutions. A website at www.springeronline.com/1-85233-896-2 gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite for the book is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to useful modern methods such as the bootstrap. This will be a key text for undergraduates in Computer Science, Physics, Mathematics, Chemistry, Biology and Business Studies who are studying a mathematical statistics course, and also for more intensive engineering statistics courses for undergraduates in all engineering subjects. Note de contenu : Contents 1 Why Probability and Statistics? 2 Outcomes, Events and Probability 3 Conditional Probability and Independence 4 Discrete Random Variables 5 Continuous Random Variables 6 Simulation 7 Expectation and Variance 8 Computations with Random Variables 9 Joint Distributions and Independence 10 Covariance and Correlation 11 More Computations with More Random Variables 12 The Poisson Process 13 The Law of Large Numbers 14 The Central Limit Theorem 15 Exploratory Data Analysis: Graphical Summaries 16 Exploratory Data Analysis: Numerical Summaries 17 Basic Statistical Models 18 The Bootstrap 19 Unbiased Estimators 20 Efficiency and Mean Squared Error 21 Maximum Likelihood 22 The Method of Least Squares 23 Confidence Intervals for the Mean 24 More on Confidence Intervals 25 Testing Hypotheses: Essentials 26 Testing Hypotheses: Elaboration 27 The t-test 28 Comparing Two Samples A: Summary of distributions B: Tables of the normal and t-distributions C: Answers to selected exercices D: Full solutions to selected exercises -Index

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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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Partial differential equations Vol. IV / Yu. V. Egorov

Public ISBD Titre : Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations Type de document : texte imprimé Auteurs : Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur Editeur : New York : Springer-Verlag Année de publication : 1993 Collection : Encyclopaedia of Mathematical Sciences Importance : 241 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-53363-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. Note de contenu : Contents Chapter 1 Microlocal properties of distributions Chapter 2 Pseudodifferential operators Chapter 3 Fourier integral operators Chapter 4 The propagation of singularities Chapter 5 Solvability of (pseudo) differntial équations Chapter 6 Smoothness of solutions of differential équations Chapter 7 Transformation of boundary-value problems Chapter 8 Hyperfunctions Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations [texte imprimé] / Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur . - New York : Springer-Verlag, 1993 . - 241 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISBN : 978-3-540-53363-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. Note de contenu : Contents Chapter 1 Microlocal properties of distributions Chapter 2 Pseudodifferential operators Chapter 3 Fourier integral operators Chapter 4 The propagation of singularities Chapter 5 Solvability of (pseudo) differntial équations Chapter 6 Smoothness of solutions of differential équations Chapter 7 Transformation of boundary-value problems Chapter 8 Hyperfunctions

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Partial differential equations Vol. VI / Yu. V. Egorov

Public ISBD Titre : Partial differential equations Vol. VI : elliptic and parabolic operators Type de document : texte imprimé Auteurs : Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur Editeur : New York : Springer-Verlag Année de publication : 1994 Collection : Encyclopaedia of Mathematical Sciences Importance : 325 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-54678-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject. Note de contenu : Contents I. Elliptic Operators on Closed Manifolds. II. Degenerate Elliptic Equations and Boundary Problems. III. Parabolic Equations. Author Index. Partial differential equations Vol. VI : elliptic and parabolic operators [texte imprimé] / Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur . - New York : Springer-Verlag, 1994 . - 325 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISSN : 978-3-540-54678-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject. Note de contenu : Contents I. Elliptic Operators on Closed Manifolds. II. Degenerate Elliptic Equations and Boundary Problems. III. Parabolic Equations. Author Index.

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Several complex variables Vol. VII / H. Grauert

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Random number generation and Monte Carlo methods / James E. Gentle

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Fundamentals of semiconductor lasers / Takahiro Numai

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Solid-state lasers / Walter Koechner

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Morphological image analysis / Pierre Soille

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High-Frequency Bipolar Transistors / M. Reisch

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Circuit design for reliability / Ricardo Reis

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CMOS capacitive sensors for lab-on-chip applications / Ebrahim Ghafar-Zadeh

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Logic Synthesis and Verification Algorithms / Gary D. Hachtel

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Probability for Statisticians / Galen R. Shorack

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