Author: Adriano M. Garsia
Publisher:
ISBN:
Category : Inequalities (Mathematics).
Languages : en
Pages : 200

Get Book

Book Description

Author: Adam Osękowski
Publisher: Springer Science & Business Media
ISBN: 3034803702
Category : Mathematics
Languages : en
Pages : 471

Get Book

Book Description
This monograph is a presentation of 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 80s, enables 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 deep implications to the geometric function theory); the boundedness of two-dimensional Hilbert transform 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 few separate parts. In the introductory chapter we present 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; the square and maximal functions. Each chapter contains additional bibliographical notes included for reference.​

Author: Laurent Mazliak
Publisher: Springer Nature
ISBN: 3031059883
Category : Mathematics
Languages : en
Pages : 419

Get Book

Book Description
Over the past eighty years, martingales have become central in the mathematics of randomness. They appear in the general theory of stochastic processes, in the algorithmic theory of randomness, and in some branches of mathematical statistics. Yet little has been written about the history of this evolution. This book explores some of the territory that the history of the concept of martingales has transformed. The historian of martingales faces an immense task. We can find traces of martingale thinking at the very beginning of probability theory, because this theory was related to gambling, and the evolution of a gambler’s holdings as a result of following a particular strategy can always be understood as a martingale. More recently, in the second half of the twentieth century, martingales became important in the theory of stochastic processes at the very same time that stochastic processes were becoming increasingly important in probability, statistics and more generally in various applied situations. Moreover, a history of martingales, like a history of any other branch of mathematics, must go far beyond an account of mathematical ideas and techniques. It must explore the context in which the evolution of ideas took place: the broader intellectual milieux of the actors, the networks that already existed or were created by the research, even the social and political conditions that favored or hampered the circulation and adoption of certain ideas. This books presents a stroll through this history, in part a guided tour, in part a random walk. First, historical studies on the period from 1920 to 1950 are presented, when martingales emerged as a distinct mathematical concept. Then insights on the period from 1950 into the 1980s are offered, when the concept showed its value in stochastic processes, mathematical statistics, algorithmic randomness and various applications.

Author: P. Hall
Publisher: Academic Press
ISBN: 1483263223
Category : Mathematics
Languages : en
Pages : 321

Get Book

Book Description
Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775939
Category : Mathematics
Languages : en
Pages : 498

Get Book

Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.

Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775946
Category : Mathematics
Languages : en
Pages : 412

Get Book

Book Description
Now available in paperback for the first time; essential reading for all students of probability theory.

Author: Ferenc Weisz
Publisher: Springer
ISBN: 3540482954
Category : Mathematics
Languages : en
Pages : 228

Get Book

Book Description
This book deals with the theory of one- and two-parameter martingale Hardy spaces and their use in Fourier analysis, and gives a summary of the latest results in this field. A method that can be applied for both one- and two-parameter cases, the so-called atomic decomposition method, is improved and provides a new and common construction of the theory of one- and two-parameter martingale Hardy spaces. A new proof of Carleson's convergence result using martingale methods for Fourier series is given with martingale methods. The book is accessible to readers familiar with the fundamentals of probability theory and analysis. It is intended for researchers and graduate students interested in martingale theory, Fourier analysis and in the relation between them.

Author: C. Dellacherie
Publisher: Elsevier
ISBN: 9780080871837
Category : Computers
Languages : en
Pages : 482

Get Book

Book Description
Probabilities and Potential, B

Author: Yu. V. Borovskikh
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110944685
Category : Mathematics
Languages : en
Pages : 336

Get Book

Book Description
No detailed description available for "Martingale Approximation".

Author: Gilles Pisier
Publisher: Cambridge University Press
ISBN: 1107137241
Category : Mathematics
Languages : en
Pages : 591

Get Book

Book Description
This book focuses on applications of martingales to the geometry of Banach spaces, and is accessible to graduate students.