Two Parameter Martingales And Their Quadratic Variation
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Two Parameter Martingales And Their Quadratic Variation
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Author : Peter Imkeller
language : en
Publisher: Springer
Release Date : 2006-11-15
Two Parameter Martingales And Their Quadratic Variation written by Peter Imkeller and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
This book has two-fold aims. In a first part it gives an introductory, thorough and essentially self-contained treatment of the general theory of two-parameter processes that has developed since around 1975. Apart from two survey papers by Merzbach and Meyer it is the first text of this kind. The second part presents the results of recent research by the author on martingale theory and stochastic calculus for two-parameter processes. Both the results and the methods of these two chapters are almost entirely new, and are of particular interest. They provide the fundamentals of a general stochastic analysis of two-parameter processes including, in particular, so far inaccessible jump phenomena. The typical rader is assumed to have some basic knowledge of the general theory of one-parameter martingales. The book should be accessible to probabilistically interested mathematicians who a) wish to become acquainted with or have a complete treatment of the main features of the general theory of two-parameter processes and basics of their stochastic calculus, b) intend to learn about the most recent developments in this area.
Two Parameter Martingales And Their Quadratic Variation
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Author :
language : en
Publisher:
Release Date : 1988
Two Parameter Martingales And Their Quadratic Variation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.
Annotation. This book has two-fold aims. In a first part it gives an introductory, thorough and essentially self-contained treatment of the general theory of two-parameter processes that has developed since around 1975. Apart from two survey papers by Merzbach and Meyer it is the first text of this kind. The second part presents the results of recent research by the author on martingale theory and stochastic calculus for two-parameter processes. Both the results and the methods of these two chapters are almost entirely new, and are of particular interest. They provide the fundamentals of a general stochastic analysis of two-parameter processes including, in particular, so far inaccessible jump phenomena. The typical rader is assumed to have some basic knowledge of the general theory of one-parameter martingales. The book should be accessible to probabilistically interested mathematicians who a) wish to become acquainted with or have a complete treatment of the main features of the general theory of two-parameter processes and basics of their stochastic calculus, b) intend to learn about the most recent developments in this area.
The Structure Of Two Parameter Martingales And Their Quadratic Variation
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Author : Peter Imkeller
language : en
Publisher:
Release Date : 1986
The Structure Of Two Parameter Martingales And Their Quadratic Variation written by Peter Imkeller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
On The Quadratic Variation Of Two Parameter Continuous Martingales
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Author : David Nualart
language : en
Publisher:
Release Date : 1982
On The Quadratic Variation Of Two Parameter Continuous Martingales written by David Nualart and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Set Indexed Martingales
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Author : B.G. Ivanoff
language : en
Publisher: CRC Press
Release Date : 1999-10-27
Set Indexed Martingales written by B.G. Ivanoff and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-27 with Mathematics categories.
Set-Indexed Martingales offers a unique, comprehensive development of a general theory of Martingales indexed by a family of sets. The authors establish-for the first time-an appropriate framework that provides a suitable structure for a theory of Martingales with enough generality to include many interesting examples. Developed from first principles, the theory brings together the theories of Martingales with a directed index set and set-indexed stochastic processes. Part One presents several classical concepts extended to this setting, including: stopping, predictability, Doob-Meyer decompositions, martingale characterizations of the set-indexed Poisson process, and Brownian motion. Part Two addresses convergence of sequences of set-indexed processes and introduces functional convergence for processes whose sample paths live in a Skorokhod-type space and semi-functional convergence for processes whose sample paths may be badly behaved. Completely self-contained, the theoretical aspects of this work are rich and promising. With its many important applications-especially in the theory of spatial statistics and in stochastic geometry- Set Indexed Martingales will undoubtedly generate great interest and inspire further research and development of the theory and applications.
Probability Theory And Its Applications In China
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Author : Shijian Yan
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Probability Theory And Its Applications In China written by Shijian Yan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Probability theory has always been an active field of research in China, but, until recently, almost all of this research was written in Chinese. This book contains surveys by some of China's leading probabilists, with a fairly complete coverage of theoretical probability and selective coverage of applied topics. The purpose of the book is to provide an account of the most significant results in probability obtained in China in the past few decades and to promote communication between probabilists in China and those in other countries. This collection will be of interest to graduate students and researchers in mathematics and probability theory, as well as to researchers in such areas as physics, engineering, biochemistry, and information science. Among the topics covered here are: stochastic analysis, stochastic differential equations, Dirichlet forms, Brownian motion and diffusion, potential theory, geometry of manifolds, semi-martingales, jump Markov processes, interacting particle systems, entropy production of Markov processes, renewal sequences and p-functions, multi-parameter stochastic processes, stationary random fields, limit theorems, strong approximations, large deviations, stochastic control systems, and probability problems in information theory.
Martingale Hardy Spaces And Their Applications In Fourier Analysis
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Author : Ferenc Weisz
language : en
Publisher: Springer
Release Date : 2006-11-15
Martingale Hardy Spaces And Their Applications In Fourier Analysis written by Ferenc Weisz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Topics In Spatial Stochastic Processes
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Author : Vincenzo Capasso
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-01-21
Topics In Spatial Stochastic Processes written by Vincenzo Capasso and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-21 with Mathematics categories.
The theory of stochastic processes indexed by a partially ordered set has been the subject of much research over the past twenty years. The objective of this CIME International Summer School was to bring to a large audience of young probabilists the general theory of spatial processes, including the theory of set-indexed martingales and to present the different branches of applications of this theory, including stochastic geometry, spatial statistics, empirical processes, spatial estimators and survival analysis. This theory has a broad variety of applications in environmental sciences, social sciences, structure of material and image analysis. In this volume, the reader will find different approaches which foster the development of tools to modelling the spatial aspects of stochastic problems.
Discrete Parameter Martingales
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Author : Jacques Neveu
language : en
Publisher: Elsevier Science & Technology
Release Date : 1975
Discrete Parameter Martingales written by Jacques Neveu and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Summability Of Multi Dimensional Fourier Series And Hardy Spaces
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Author : Ferenc Weisz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Summability Of Multi Dimensional Fourier Series And Hardy Spaces written by Ferenc Weisz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The history of martingale theory goes back to the early fifties when Doob [57] pointed out the connection between martingales and analytic functions. On the basis of Burkholder's scientific achievements the mar tingale theory can perfectly well be applied in complex analysis and in the theory of classical Hardy spaces. This connection is the main point of Durrett's book [60]. The martingale theory can also be well applied in stochastics and mathematical finance. The theories of the one-parameter martingale and the classical Hardy spaces are discussed exhaustively in the literature (see Garsia [83], Neveu [138], Dellacherie and Meyer [54, 55], Long [124], Weisz [216] and Duren [59], Stein [193, 194], Stein and Weiss [192], Lu [125], Uchiyama [205]). The theory of more-parameter martingales and martingale Hardy spaces is investigated in Imkeller [107] and Weisz [216]. This is the first mono graph which considers the theory of more-parameter classical Hardy spaces. The methods of proofs for one and several parameters are en tirely different; in most cases the theorems stated for several parameters are much more difficult to verify. The so-called atomic decomposition method that can be applied both in the one-and more-parameter cases, was considered for martingales by the author in [216].