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Limit sets of dynamical systems on the space of probability measures

✍ Scribed by Abraham Boyarsky

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
335 KB
Volume
14
Category
Article
ISSN
0022-0396

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πŸ“œ SIMILAR VOLUMES

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## Abstract The space of probability measures on a Riemannian manifold is endowed with the Fisher information metric. In [4] T. Friedrich showed that this space admits also Poisson structures {, }. In this note, we give directly another proof for the structure {, } being Poisson. (Β© 2007 WILEY‐VCH

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In this paper we consider a Hamiltonian H on P 2 (R 2d ), the set of probability measures with finite quadratic moments on the phase space R 2d = R d Γ— R d , which is a metric space when endowed with the Wasserstein distance W 2 . We study the initial value problem dΒ΅ t /dt +βˆ‡β€’(J d v t Β΅ t ) = 0, wh

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## Some interesting properties of an indexed family of probability junctions {P,} whose application to the theory of pattern recognition as given by Cooper (1) are presented. It is shown that as m approaches in$nity P, converges to a well-defined probability function on En. !