Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Semimartingales (Mathematics) --- Stochastic analysis. --- Brownian motion processes. --- Semimartingales (Mathématiques) --- Analyse stochastique --- Mouvement brownien, Processus de

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Library science --- Information science --- Bibliothéconomie --- Sciences de l'information --- Encyclopedias. --- Encyclopédies --- Bibliothéconomie --- Encyclopédies --- Semimartingales (Mathematics) --- Statistique mathématique --- Semimartingales (Mathématiques) --- Asymptotic theory --- Théorie asymptotique --- -Semimartingales --- Statistique mathématique --- Semimartingales (Mathématiques) --- Théorie asymptotique --- Stochastic processes --- Mathematical statistics --- Library science - Encyclopedias --- Information science - Encyclopedias

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an introduction to the theory of martingales and semimartingales, random measures stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. The second edition contains some additions to the text and references. Some parts are completely rewritten.

Stochastic processes --- Limit theorems (Probability theory) --- Semimartingales (Mathematics) --- Limit theorems (Probability theory). --- Semimartingales (Mathematics). --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This monograph presents a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 1980s, makes it possible to deduce a given inequality for semimartingales from the existence of a certain special function with some convex-type properties. Remarkably, an appropriate application of the method leads to the sharp version of the estimate under investigation, which is particularly important for applications. These include the theory of quasiregular mappings (with major implications for the geometric function theory); the boundedness of two-dimensional Hilbert transforms and a more general class of Fourier multipliers; the theory of rank-one convex and quasiconvex functions; and more. The book is divided into a number of distinct parts. In the introductory chapter we present the motivation for the results and relate them to some classical problems in harmonic analysis. The next part contains a general description of the method, which is applied in subsequent chapters to the study of sharp estimates for discrete-time martingales; discrete-time sub- and supermartingales; continuous time processes; and the square and maximal functions. Each chapter contains additional bibliographical notes included for reference purposes.

Functional analysis. --- Mathematics. --- Semimartingales (Mathematics). --- Stochastic inequalities. --- Semimartingales (Mathematics) --- Stochastic inequalities --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Martingales (Mathematics) --- Stochastic processes. --- Random processes --- Potential theory (Mathematics). --- Probabilities. --- Probability Theory and Stochastic Processes. --- Potential Theory. --- Functional Analysis. --- Probabilities --- Stochastic processes --- Distribution (Probability theory. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes.   One of the basic aims of theory of probability and statistics is to build stochastic models which explain the phenomenon under investigation and explore the dependence among various covariates which influence this phenomenon. Classic examples are the concepts of Markov dependence or of mixing for random processes. Esary, Proschan and Walkup introduced the concept of association for random variables, and Newman and Wright studied properties of processes termed as demimartingales. It can be shown that the partial sums of mean zero associated random variables form a demimartingale.   Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to problems in nonparametric statistical inference for such processes are investigated in the last three chapters.   This book will appeal to graduate students and researchers interested in probabilistic aspects of various types of stochastic processes and their applications in reliability theory, statistical mechanics, percolation theory and other areas.

Probabilities. --- Sequences (Mathematics). --- Probabilities --- Sequences (Mathematics) --- Semimartingales (Mathematics) --- Nonparametric statistics --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Nonparametric statistics. --- Random variables. --- Chance variables --- Stochastic variables --- Probability --- Statistical inference --- Distribution-free statistics --- Statistics, Distribution-free --- Statistics, Nonparametric --- Mathematics. --- Probability Theory and Stochastic Processes. --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Variables (Mathematics) --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions