NDLI: Choices and intervals

Content Provider	Springer Nature Link
Author	Maillard, Pascal Paquette, Elliot
Copyright Year	2016
Abstract	We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals goes to infinity. We give a characterization of this limit as a solution of an ODE and use this to derive precise tail estimates. The convergence is established by showing that the size-biased empirical distribution evolves in the limit according to a certain deterministic evolution equation. Although this equation involves a non-local, non-linear operator, it can be studied thanks to a carefully chosen norm with respect to which this operator is contractive.In finite-dimensional settings, convergence results like this usually go under the name of stochastic approximation and can be approached by a general method of Kushner and Clark. An important technical contribution of this article is the extension of this method to an infinite-dimensional setting.
Starting Page	337
Ending Page	384
Page Count	48
File Format	PDF
ISSN	00212172
Journal	Israel Journal of Mathematics
Volume Number	212
Issue Number	1
e-ISSN	15658511
Language	English
Publisher	The Hebrew University Magnes Press
Publisher Date	2016-01-07
Publisher Place	Jerusalem
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematics Algebra Group Theory and Generalizations Analysis Applications of Mathematics Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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