• K B Athreya

Articles written in Proceedings – Mathematical Sciences

• Iterations of random and deterministic functions

Letf be a probability generating function on [0, 1]. The convergence of its iteratesfn to fixed points is studied in this paper. Results include rates forf andf-1. Also iterates of independent identically distributed stable processes are studied and a trichotomy based on the order of the stability is established.

• Entropy Maximization

It is shown that (i) every probability density is the unique maximizer of relative entropy in an appropriate class and (ii) in the class of all pdf 𝑓 that satisfy $\int fh_id_\mu=\lambda_i$ for $i=1,2,\ldots,\ldots k$ the maximizer of entropy is an $f_0$ that is proportional to $\exp(\sum c_i h_i)$ for some choice of $c_i$. An extension of this to a continuum of constraints and many examples are presented.

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019