• K B Athreya

      Articles written in Proceedings – Mathematical Sciences

    • Iterations of random and deterministic functions

      K B Athreya

      More Details Abstract Fulltext PDF

      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

      K B Athreya

      More Details Abstract Fulltext PDF

      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.

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