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Dynamic random walks in Clifford algebras

Dynamic random walks in Clifford algebras Abstract Given a Clifford algebra of arbitrary signature ℓ p,q , p + q = n , multiplicative random walks with dynamic transitions are induced by sequences of random variables taking values in the unit basis vectors and paravectors of the algebra. These walks can be viewed as random walks on “directed hypercubes”. Properties of such multiplicative walks are investigated, and these multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Pure and Applied Mathematics de Gruyter

Dynamic random walks in Clifford algebras

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Publisher
de Gruyter
Copyright
Copyright © 2010 by the
ISSN
1867-1152
eISSN
1869-6090
DOI
10.1515/apam.2010.007
Publisher site
See Article on Publisher Site

Abstract

Abstract Given a Clifford algebra of arbitrary signature ℓ p,q , p + q = n , multiplicative random walks with dynamic transitions are induced by sequences of random variables taking values in the unit basis vectors and paravectors of the algebra. These walks can be viewed as random walks on “directed hypercubes”. Properties of such multiplicative walks are investigated, and these multiplicative walks are then summed to induce additive walks on the algebra. Properties of both types of walks are considered, and limit theorems are developed.

Journal

Advances in Pure and Applied Mathematicsde Gruyter

Published: Mar 1, 2010

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