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Derivation And Martingales
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Book Synopsis Derivation and Martingales by : Charles A. Hayes
Download or read book Derivation and Martingales written by Charles A. Hayes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Part I of this report the pointwise derivation of scalar set functions is investigated, first along the lines of R. DE POSSEL (abstract derivation basis) and A. P. MORSE (blankets); later certain concrete situations (e. g. , the interval basis) are studied. The principal tool is a Vitali property, whose precise form depends on the derivation property studied. The "halo" (defined at the beginning of Part I, Ch. IV) properties can serve to establish a Vitali property, or sometimes produce directly a derivation property. The main results established are the theorem of JESSEN-MARCINKIEWICZ-ZYGMUND (Part I, Ch. V) and the theorem of A. P. MORSE on the universal derivability of star blankets (Ch. VI) . . In Part II, points are at first discarded; the setting is somatic. It opens by treating an increasing stochastic basis with directed index sets (Th. I. 3) on which premartingales, semimartingales and martingales are defined. Convergence theorems, due largely to K. KRICKEBERG, are obtained using various types of convergence: stochastic, in the mean, in Lp-spaces, in ORLICZ spaces, and according to the order relation. We may mention in particular Th. II. 4. 7 on the stochastic convergence of a submartingale of bounded variation. To each theorem for martingales and semi-martingales there corresponds a theorem in the atomic case in the theory of cell (abstract interval) functions. The derivates concerned are global. Finally, in Ch.
Book Synopsis Derivation and Martingales by : C. A. Hayes
Download or read book Derivation and Martingales written by C. A. Hayes and published by . This book was released on 1985 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Martingales And Stochastic Analysis by : James J Yeh
Download or read book Martingales And Stochastic Analysis written by James J Yeh and published by World Scientific. This book was released on 1995-12-08 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a thorough and self-contained treatise of martingales as a tool in stochastic analysis, stochastic integrals and stochastic differential equations. The book is clearly written and details of proofs are worked out.
Book Synopsis Introduction to Global Variational Geometry by : Demeter Krupka
Download or read book Introduction to Global Variational Geometry written by Demeter Krupka and published by Elsevier. This book was released on 2000-04-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Book Synopsis Probability in Banach Spaces V by : Anatole Beck
Download or read book Probability in Banach Spaces V written by Anatole Beck and published by Springer. This book was released on 2006-11-14 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Statistical Methods for Case-Control Studies by : Ørnulf Borgan
Download or read book Handbook of Statistical Methods for Case-Control Studies written by Ørnulf Borgan and published by CRC Press. This book was released on 2018-06-27 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Statistical Methods for Case-Control Studies is written by leading researchers in the field. It provides an in-depth treatment of up-to-date and currently developing statistical methods for the design and analysis of case-control studies, as well as a review of classical principles and methods. The handbook is designed to serve as a reference text for biostatisticians and quantitatively-oriented epidemiologists who are working on the design and analysis of case-control studies or on related statistical methods research. Though not specifically intended as a textbook, it may also be used as a backup reference text for graduate level courses. Book Sections Classical designs and causal inference, measurement error, power, and small-sample inference Designs that use full-cohort information Time-to-event data Genetic epidemiology About the Editors Ørnulf Borgan is Professor of Statistics, University of Oslo. His book with Andersen, Gill and Keiding on counting processes in survival analysis is a world classic. Norman E. Breslow was, at the time of his death, Professor Emeritus in Biostatistics, University of Washington. For decades, his book with Nick Day has been the authoritative text on case-control methodology. Nilanjan Chatterjee is Bloomberg Distinguished Professor, Johns Hopkins University. He leads a broad research program in statistical methods for modern large scale biomedical studies. Mitchell H. Gail is a Senior Investigator at the National Cancer Institute. His research includes modeling absolute risk of disease, intervention trials, and statistical methods for epidemiology. Alastair Scott was, at the time of his death, Professor Emeritus of Statistics, University of Auckland. He was a major contributor to using survey sampling methods for analyzing case-control data. Chris J. Wild is Professor of Statistics, University of Auckland. His research includes nonlinear regression and methods for fitting models to response-selective data.
Book Synopsis Stopping Times and Directed Processes by : Gerald A. Edgar
Download or read book Stopping Times and Directed Processes written by Gerald A. Edgar and published by Cambridge University Press. This book was released on 1992-08-28 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of the theory of 'stopping times' for probability theorists and statisticians.
Book Synopsis Analysis of Infectious Disease Data by : N.G. Becker
Download or read book Analysis of Infectious Disease Data written by N.G. Becker and published by CRC Press. This book was released on 2017-11-22 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives an up-to-date account of various approaches availablefor the analysis of infectious disease data. Most of the methods havebeen developed only recently, and for those based on particularlymodern mathematics, details of the computation are carefullyillustrated. Interpretation is discussed at some length and the emphasisthroughout is on making statistical inferences about epidemiologicallyimportant parameters.Niels G. Becker is Reader in Statistics at La Trobe University,Australia.
Book Synopsis Continuous Martingales and Brownian Motion by : Daniel Revuz
Download or read book Continuous Martingales and Brownian Motion written by Daniel Revuz and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the probabilistic theory ofBrownian motion. This is a good topic to center a discussion around because Brownian motion is in the intersec tioll of many fundamental classes of processes. It is a continuous martingale, a Gaussian process, a Markov process or more specifically a process with in dependent increments; it can actually be defined, up to simple transformations, as the real-valued, centered process with independent increments and continuous paths. It is therefore no surprise that a vast array of techniques may be success fully applied to its study and we, consequently, chose to organize the book in the following way. After a first chapter where Brownian motion is introduced, each of the following ones is devoted to a new technique or notion and to some of its applications to Brownian motion. Among these techniques, two are of para mount importance: stochastic calculus, the use ofwhich pervades the whole book and the powerful excursion theory, both of which are introduced in a self contained fashion and with a minimum of apparatus. They have made much easier the proofs of many results found in the epoch-making book of Itö and McKean: Diffusion Processes and their Sampie Paths, Springer (1965).
Book Synopsis Martingales and Stochastic Integrals by : Paul André Meyer
Download or read book Martingales and Stochastic Integrals written by Paul André Meyer and published by Springer. This book was released on 1972 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book contains a preliminary version (the second draft) of the first two chapters of a book on martingales and stochastic integrals. If the following chapters are ever written, it will be as a joint work with Cl. Dellacherie ... The next installment then will be on stochastic integrals."--Introduction.
Book Synopsis Set-Indexed Martingales by : B.G. Ivanoff
Download or read book Set-Indexed Martingales written by B.G. Ivanoff and published by CRC Press. This book was released on 1999-10-27 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Brownian Motion and Martingales in Analysis by : Richard Durrett
Download or read book Brownian Motion and Martingales in Analysis written by Richard Durrett and published by Wadsworth Publishing Company. This book was released on 1984 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Probability Theory by : Yuan Shih Chow
Download or read book Probability Theory written by Yuan Shih Chow and published by Springer Science & Business Media. This book was released on 2012-11-28 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising the major theorems of probability theory and the measure theoretical foundations of the subject, the main topics treated here are independence, interchangeability, and martingales. Particular emphasis is placed upon stopping times, both as tools in proving theorems and as objects of interest themselves. No prior knowledge of measure theory is assumed and a unique feature of the book is the combined presentation of measure and probability. It is easily adapted for graduate students familiar with measure theory using the guidelines given. Special features include: - A comprehensive treatment of the law of the iterated logarithm - The Marcinklewicz-Zygmund inequality, its extension to martingales and applications thereof - Development and applications of the second moment analogue of Walds equation - Limit theorems for martingale arrays; the central limit theorem for the interchangeable and martingale cases; moment convergence in the central limit theorem - Complete discussion, including central limit theorem, of the random casting of r balls into n cells - Recent martingale inequalities - Cram r-L vy theorem and factor-closed families of distributions.
Book Synopsis Introduction to Stochastic Calculus with Applications by : Fima C. Klebaner
Download or read book Introduction to Stochastic Calculus with Applications written by Fima C. Klebaner and published by Imperial College Press. This book was released on 2005 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a concise treatment of stochastic calculus and its applications. It gives a simple but rigorous treatment of the subject including a range of advanced topics, it is useful for practitioners who use advanced theoretical results. It covers advanced applications, such as models in mathematical finance, biology and engineering.Self-contained and unified in presentation, the book contains many solved examples and exercises. It may be used as a textbook by advanced undergraduates and graduate students in stochastic calculus and financial mathematics. It is also suitable for practitioners who wish to gain an understanding or working knowledge of the subject. For mathematicians, this book could be a first text on stochastic calculus; it is good companion to more advanced texts by a way of examples and exercises. For people from other fields, it provides a way to gain a working knowledge of stochastic calculus. It shows all readers the applications of stochastic calculus methods and takes readers to the technical level required in research and sophisticated modelling.This second edition contains a new chapter on bonds, interest rates and their options. New materials include more worked out examples in all chapters, best estimators, more results on change of time, change of measure, random measures, new results on exotic options, FX options, stochastic and implied volatility, models of the age-dependent branching process and the stochastic Lotka-Volterra model in biology, non-linear filtering in engineering and five new figures.Instructors can obtain slides of the text from the author.
Book Synopsis A Course of Stochastic Analysis by : Alexander Melnikov
Download or read book A Course of Stochastic Analysis written by Alexander Melnikov and published by Springer Nature. This book was released on 2023-04-02 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.
Book Synopsis Quantitative Modeling of Derivative Securities by : Peter Laurence
Download or read book Quantitative Modeling of Derivative Securities written by Peter Laurence and published by Routledge. This book was released on 2017-11-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative Modeling of Derivative Securities demonstrates how to take the basic ideas of arbitrage theory and apply them - in a very concrete way - to the design and analysis of financial products. Based primarily (but not exclusively) on the analysis of derivatives, the book emphasizes relative-value and hedging ideas applied to different financial instruments. Using a ""financial engineering approach,"" the theory is developed progressively, focusing on specific aspects of pricing and hedging and with problems that the technical analyst or trader has to consider in practice. More than just an introductory text, the reader who has mastered the contents of this one book will have breached the gap separating the novice from the technical and research literature.
Book Synopsis Nonlinear Filtering and Smoothing by : Venkatarama Krishnan
Download or read book Nonlinear Filtering and Smoothing written by Venkatarama Krishnan and published by Courier Corporation. This book was released on 2013-10-17 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most useful for graduate students in engineering and finance who have a basic knowledge of probability theory, this volume is designed to give a concise understanding of martingales, stochastic integrals, and estimation. It emphasizes applications. Many theorems feature heuristic proofs; others include rigorous proofs to reinforce physical understanding. Numerous end-of-chapter problems enhance the book's practical value. After introducing the basic measure-theoretic concepts of probability and stochastic processes, the text examines martingales, square integrable martingales, and stopping times. Considerations of white noise and white-noise integrals are followed by examinations of stochastic integrals and stochastic differential equations, as well as the associated Ito calculus and its extensions. After defining the Stratonovich integral, the text derives the correction terms needed for computational purposes to convert the Ito stochastic differential equation to the Stratonovich form. Additional chapters contain the derivation of the optimal nonlinear filtering representation, discuss how the Kalman filter stands as a special case of the general nonlinear filtering representation, apply the nonlinear filtering representations to a class of fault-detection problems, and discuss several optimal smoothing representations.
