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.
Download or read book Topics in Spatial Stochastic Processes written by Vincenzo Capasso and published by Springer Science & Business Media. This book was released on 2003-01-21 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory of Random Sets written by Ilya Molchanov and published by Springer Science & Business Media. This book was released on 2005-11-28 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
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.
Download or read book The Splendors and Miseries of Martingales written by Laurent Mazliak and published by Springer Nature. This book was released on 2022-10-17 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sequential Stochastic Optimization written by R. Cairoli and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and solved.Offering much material that is either new or has never beforeappeared in book form, it lucidly presents a unified theory ofoptimal stopping and optimal sequential control of stochasticprocesses. This book has been carefully organized so that littleprior knowledge of the subject is assumed; its only prerequisitesare a standard graduate course in probability theory and somefamiliarity with discrete-parameter martingales. Major topics covered in Sequential Stochastic Optimization include: * Fundamental notions, such as essential supremum, stopping points,accessibility, martingales and supermartingales indexed by INd * Conditions which ensure the integrability of certain suprema ofpartial sums of arrays of independent random variables * The general theory of optimal stopping for processes indexed byInd * Structural properties of information flows * Sequential sampling and the theory of optimal sequential control * Multi-armed bandits, Markov chains and optimal switching betweenrandom walks
Download or read book Modern Mathematics and Mechanics written by Victor A. Sadovnichiy and published by Springer. This book was released on 2018-11-29 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical systems. These abstract mathematical approaches are applied to problem-solving in solid mechanics, hydro- and aerodynamics, optimization, decision making theory and control theory. This volume is therefore relevant to mathematicians as well as engineers working at the interface of these fields.
Download or read book Random Walk Brownian Motion and Martingales written by Rabi Bhattacharya and published by Springer Nature. This book was released on 2021-09-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers an approachable introduction to stochastic processes that explores the four pillars of random walk, branching processes, Brownian motion, and martingales. Building from simple examples, the authors focus on developing context and intuition before formalizing the theory of each topic. This inviting approach illuminates the key ideas and computations in the proofs, forming an ideal basis for further study. Consisting of many short chapters, the book begins with a comprehensive account of the simple random walk in one dimension. From here, different paths may be chosen according to interest. Themes span Poisson processes, branching processes, the Kolmogorov–Chentsov theorem, martingales, renewal theory, and Brownian motion. Special topics follow, showcasing a selection of important contemporary applications, including mathematical finance, optimal stopping, ruin theory, branching random walk, and equations of fluids. Engaging exercises accompany the theory throughout. Random Walk, Brownian Motion, and Martingales is an ideal introduction to the rigorous study of stochastic processes. Students and instructors alike will appreciate the accessible, example-driven approach. A single, graduate-level course in probability is assumed.
Download or read book Multiparameter Processes written by Davar Khoshnevisan and published by Springer Science & Business Media. This book was released on 2006-04-10 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics
Download or read book Math Everywhere written by G. Aletti and published by Springer Science & Business Media. This book was released on 2007-07-11 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings report on the conference "Math Everywhere", celebrating the 60th birthday of the mathematician Vincenzo Capasso. The conference promoted ideas Capasso has pursued and shared the open atmosphere he is known for. Topic sections include: Deterministic and Stochastic Systems. Mathematical Problems in Biology, Medicine and Ecology. Mathematical Problems in Industry and Economics. The broad spectrum of contributions to this volume demonstrates the truth of its title: Math is Everywhere, indeed.
Download or read book Asymptotic Laws and Methods in Stochastics written by Donald Dawson and published by Springer. This book was released on 2015-11-12 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.
Download or read book Stochastic Models written by Donald Andrew Dawson and published by American Mathematical Soc.. This book was released on 2000 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the refereed proceedings of the International Conference on Stochastic Models held in Ottawa (ON, Canada) in honor of Professor Donald A. Dawson. Contributions to the volume were written by students and colleagues of Professor Dawson, many of whom are eminent researchers in their own right. A main theme of the book is the development and study of the Dawson-Watanabe "superprocess", a fundamental building block in modelling interaction particle systems undergoing reproduction and movement. The volume also contains an excellent review article by Professor Dawson and a complete list of his work. This comprehensive work offers a wide assortment of articles on Markov processes, branching processes, mathematical finance, filtering, queueing networks, time series, and statistics. It should be of interest to a broad mathematical audience.
Download or read book Bulletin Institute of Mathematical Statistics written by Institute of Mathematical Statistics and published by . This book was released on 1993 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Trends in Applied Harmonic Analysis Volume 2 written by Akram Aldroubi and published by Springer Nature. This book was released on 2019-11-26 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume collects papers based on courses and talks given at the 2017 CIMPA school Harmonic Analysis, Geometric Measure Theory and Applications, which took place at the University of Buenos Aires in August 2017. These articles highlight recent breakthroughs in both harmonic analysis and geometric measure theory, particularly focusing on their impact on image and signal processing. The wide range of expertise present in these articles will help readers contextualize how these breakthroughs have been instrumental in resolving deep theoretical problems. Some topics covered include: Gabor frames Falconer distance problem Hausdorff dimension Sparse inequalities Fractional Brownian motion Fourier analysis in geometric measure theory This volume is ideal for applied and pure mathematicians interested in the areas of image and signal processing. Electrical engineers and statisticians studying these fields will also find this to be a valuable resource.
Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book S minaire de Probabilit s XLVIII written by Catherine Donati-Martin and published by Springer. This book was released on 2016-11-17 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: In addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series’ focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices. Also included are some particularly interesting articles involving harmonic measures, random fields and loop soups. The featured contributors are Mathias Beiglböck, Martin Huesmann and Florian Stebegg, Nicolas Juillet, Gilles Pags, Dai Taguchi, Alexis Devulder, Mátyás Barczy and Peter Kern, I. Bailleul, Jürgen Angst and Camille Tardif, Nicolas Privault, Anita Behme, Alexander Lindner and Makoto Maejima, Cédric Lecouvey and Kilian Raschel, Christophe Profeta and Thomas Simon, O. Khorunzhiy and Songzi Li, Franck Maunoury, Stéphane Laurent, Anna Aksamit and Libo Li, David Applebaum, and Wendelin Werner.
Download or read book Measure Theory written by D. H. Fremlin and published by Torres Fremlin. This book was released on 2000 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt:
