Law of the Iterated Logarithm for some Markov operators

TL;DR

This paper proves the Law of the Iterated Logarithm for certain Markov operators that rapidly converge to an invariant measure, extending applications to models like the cell cycle.

Contribution

It establishes the LIL for specific Markov operators associated with iterated function systems, broadening theoretical understanding.

Findings

LIL holds for Markov operators with exponential convergence

Results applicable to biological models like cell cycle

Extends probabilistic limit theorems to new operator classes

Abstract

The Law of the Iterated Logarithm for some Markov operators, which converge exponentially to the invariant measure, is established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell cycle model examined by A. Lasota and M.C. Mackey, J. Math. Biol. (1999).