[PDF] Measures On Topological Semigroups Convolution Products And Random Walks eBook

Author : Göran Högnäs
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 23,4 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475723881

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A Scientific American article on chaos, see Crutchfield et al. (1986), illus trates a very persuasive example of recurrence. A painting of Henri Poincare, or rather a digitized version of it, is stretched and cut to produce a mildly distorted image of Poincare. The same procedure is applied to the distorted image and the process is repeated over and over again on the successively more and more blurred images. After a dozen repetitions nothing seems to be left of the original portrait. Miraculously, structured images appear briefly as we continue to apply the distortion procedure to successive images. After 241 iterations the original picture reappears, unchanged! Apparently the pixels of the Poincare portrait were moving about in accor dance with a strictly deterministic rule. More importantly, the set of all pixels, the whole portrait, was transformed by the distortion mechanism. In this exam ple the transformation seems to have been a reversible one since the original was faithfully recreated. It is not very farfetched to introduce a certain amount of randomness and irreversibility in the above example. Think of a random miscoloring of some pixels or of inadvertently giving a pixel the color of its neighbor. The methods in this book are geared towards being applicable to the asymp totics of such transformation processes. The transformations form a semigroup in a natural way; we want to investigate the long-term behavior of random elements of this semigroup.

Author : A. Mukherhea
Publisher :
Page : 14 pages
File Size : 29,7 MB
Release : 1973
Category :
ISBN :

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In this paper, the authors, consider a result due to M. Rosenblatt which is frequently useful in the theory of random walks. His result states that if mu is a regular probability measure on a compact semigroup S which is generated by the support of mu, then given any open set O containing an ideal of S, (mu sup n)(O) converges to 1 as n nears infinity. The essential contribution of this paper is an example of an interesting family of probability measures on the interval(0, infinity) which shows that Rosenblatt's theorem cannot be extended to a general locally compact semigroup. Of further significance in this paper is the indicated relationship between the Central Limit Theorem of probability theory on the one hand and polynomial approximation of the exponential function on the other.

Author : Göran Högnäs
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 27,1 MB
Release : 2010-11-02
Category : Mathematics
ISBN : 038777548X

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This second edition presents up-to-date material on the theory of weak convergance of convolution products of probability measures in semigroups, the theory of random walks on semigroups, and their applications to products of random matrices. In addition, this unique work examines the essentials of abstract semigroup theory and its application to concrete semigroups of matrices. This substantially revised text includes exercises at various levels at the end of each section and includes the best available proofs on the most important theorems used in a book, making it suitable for a one semester course on semigroups. In addition, it could also be used as a main text or supplementary material for courses focusing on probability on algebraic structures or weak convergance. This book is ideally suited to graduate students in mathematics, and students in other fields, such as engineering and the sciences with an interest in probability. Students in statistics using advanced probability will also find this book useful.

Author : Gregory Budzban
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 49,52 MB
Release : 2016-06-29
Category : Mathematics
ISBN : 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.