Limit Theorems for Some Markov Operators

TL;DR

This paper establishes exponential convergence rates and a Central Limit Theorem for certain Markov operators related to iterated function systems, with applications to models like the cell cycle.

Contribution

It introduces new limit theorems for Markov operators associated with iterated function systems, extending previous models such as the cell cycle.

Findings

Proves exponential convergence rates for specific Markov operators.

Establishes a Central Limit Theorem for these operators.

Provides a framework applicable to biological models like the cell cycle.

Abstract

The exponential rate of convergence and the Central Limit Theorem for some Markov operators are established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell cycle model given by Lasota & Mackey (1999).