Structural Aspects in the Theory of Probability

Structural Aspects in the Theory of Probability

Author: Herbert Heyer

Publisher: World Scientific

ISBN: 9789812389374

Category: Mathematics

Page: 388

View: 546

This book focuses on the algebraic-topological aspects of probability theory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that of the Fourier transform. This analytic tool along with the relevant parts of harmonic analysis makes it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. Graduate students, lecturers and researchers may use the book as a primer in the theory of probability measures on groups and related structures.This book has been selected for coverage in: ? CC / Physical, Chemical & Earth Sciences? Index to Scientific Book Contents? (ISBC)

Structural Aspects in the Theory of Probability

Structural Aspects in the Theory of Probability

Author: Herbert Heyer

Publisher: World Scientific

ISBN: 9789812562289

Category: Abelian groups

Page: 388

View: 887

This book focuses on the algebraic-topological aspects of probabilitytheory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroupsand the corresponding processes with independent increments

Structural Aspects in the Theory of Probability

Structural Aspects in the Theory of Probability

Author: Herbert Heyer

Publisher: World Scientific

ISBN: 9789814282482

Category: Mathematics

Page: 412

View: 714

The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

Random and Vector Measures

Random and Vector Measures

Author: Malempati Madhusudana Rao

Publisher: World Scientific

ISBN: 9789814350815

Category: Mathematics

Page: 538

View: 516

Deals with the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. This book analyzes several stationary aspects and related processes.

Probability Measures on Locally Compact Groups

Probability Measures on Locally Compact Groups

Author: H. Heyer

Publisher: Springer Science & Business Media

ISBN: 9783642667060

Category: Mathematics

Page: 532

View: 519

Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.

Random Graphs, Geometry and Asymptotic Structure

Random Graphs, Geometry and Asymptotic Structure

Author: Michael Krivelevich

Publisher: Cambridge University Press

ISBN: 9781316552940

Category: Mathematics

Page:

View: 813

The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.

Stochastic Processes

Stochastic Processes

Author: Wolfgang Paul

Publisher: Springer Science & Business Media

ISBN: 9783319003276

Category: Science

Page: 280

View: 637

This book introduces the theory of stochastic processes with applications taken from physics and finance. Fundamental concepts like the random walk or Brownian motion but also Levy-stable distributions are discussed. Applications are selected to show the interdisciplinary character of the concepts and methods. In the second edition of the book a discussion of extreme events ranging from their mathematical definition to their importance for financial crashes was included. The exposition of basic notions of probability theory and the Brownian motion problem as well as the relation between conservative diffusion processes and quantum mechanics is expanded. The second edition also enlarges the treatment of financial markets. Beyond a presentation of geometric Brownian motion and the Black-Scholes approach to option pricing as well as the econophysics analysis of the stylized facts of financial markets, an introduction to agent based modeling approaches is given.

Worldviews, Science and Us

Worldviews, Science and Us

Author: Diederik Aerts

Publisher: World Scientific

ISBN: 9789814383073

Category: Science

Page: 359

View: 137

The present volume is part of the ‘Worldviews, Science and Us’ series of proceedings. It contains selected contributions on the subject of bridging knowledge and its implications for our perspectives of the world. This volume also represents the proceedings of the interdisciplinary stream of the international workshop (Part 1) Times of Entanglement, 21–22 September 2010 at the Minsheng Art Museum in Shanghai, People's Republic of China in the context of the Shanghai World Expo 2010 and, related cutting-edge investigations in the quantum paradigm from discussion panels organized by the Leo Apostel Center for Interdisciplinary studies within the framework of the ‘Research on the Construction of Integrating Worldviews’ research community set up by the Flanders Fund for Scientific Research. Further information about this research community and a full list of the associated international research centers can be found at http: //www.vub.ac.be/CLEA/res/worldviews/.