Probability on Algebraic and Geometric Structures

Probability on Algebraic and Geometric Structures PDF

Author: Gregory Budzban

Publisher: American Mathematical Soc.

Published: 2016-06-29

Total Pages: 236

ISBN-13: 1470419459

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This volume contains the proceedings of the International Research Conference “Probability on Algebraic and Geometric Structures”, held from June 5–7, 2014, at Southern Illinois University, Carbondale, IL, celebrating the careers of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea. These proceedings include survey papers and new research on a variety of topics such as probability measures and the behavior of stochastic processes on groups, semigroups, and Clifford algebras; algebraic methods for analyzing Markov chains and products of random matrices; stochastic integrals and stochastic ordinary, partial, and functional differential equations.

Probability on Algebraic Structures

Probability on Algebraic Structures PDF

Author: Gregory Budzban

Publisher: American Mathematical Soc.

Published: 2000

Total Pages: 250

ISBN-13: 0821820273

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This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.

Probabilities on Algebraic Structures

Probabilities on Algebraic Structures PDF

Author: Ulf Grenander

Publisher: Courier Corporation

Published: 2008-01-01

Total Pages: 222

ISBN-13: 0486462870

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This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.

Stochastic and Integral Geometry

Stochastic and Integral Geometry PDF

Author: Rolf Schneider

Publisher: Springer Science & Business Media

Published: 2008-09-08

Total Pages: 692

ISBN-13: 354078859X

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Stochastic geometry deals with models for random geometric structures. Its early beginnings are found in playful geometric probability questions, and it has vigorously developed during recent decades, when an increasing number of real-world applications in various sciences required solid mathematical foundations. Integral geometry studies geometric mean values with respect to invariant measures and is, therefore, the appropriate tool for the investigation of random geometric structures that exhibit invariance under translations or motions. Stochastic and Integral Geometry provides the mathematically oriented reader with a rigorous and detailed introduction to the basic stationary models used in stochastic geometry – random sets, point processes, random mosaics – and to the integral geometry that is needed for their investigation. The interplay between both disciplines is demonstrated by various fundamental results. A chapter on selected problems about geometric probabilities and an outlook to non-stationary models are included, and much additional information is given in the section notes.

Stochastic Geometry

Stochastic Geometry PDF

Author: Wilfrid S. Kendall

Publisher: Routledge

Published: 2019-06-10

Total Pages: 419

ISBN-13: 1351413724

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Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

Geometric Aspects of Probability Theory and Mathematical Statistics

Geometric Aspects of Probability Theory and Mathematical Statistics PDF

Author: V.V. Buldygin

Publisher: Springer Science & Business Media

Published: 2000-08-31

Total Pages: 322

ISBN-13: 9780792364139

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This book demonstrates the usefulness of geometric methods in probability theory and mathematical statistics, and shows close relationships between these disciplines and convex analysis. Deep facts and statements from the theory of convex sets are discussed with their applications to various questions arising in probability theory, mathematical statistics, and the theory of stochastic processes. The book is essentially self-contained, and the presentation of material is thorough in detail. Audience: The topics considered in the book are accessible to a wide audience of mathematicians, and graduate and postgraduate students, whose interests lie in probability theory and convex geometry.

Geometric Structures of Information

Geometric Structures of Information PDF

Author: Frank Nielsen

Publisher: Springer

Published: 2018-11-19

Total Pages: 392

ISBN-13: 3030025209

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This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

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