On a problem of \"O. Stenflo
Klaudiusz Czudek, Tomasz Szarek
TL;DR
This paper constructs a specific e-chain on a locally compact space with a unique stationary distribution, demonstrating that the strong law of large numbers does not necessarily hold in this setting, thus answering a question posed by "O. Stenflo.
Contribution
It provides a counterexample to the assumption that the strong law of large numbers always applies to such chains, clarifying the limitations of existing theorems.
Findings
Counterexample of an e-chain with unique stationary distribution where the strong law fails
Clarification of conditions under which the strong law of large numbers may not hold
Answers a previously open question by "O. Stenflo
Abstract
We construct an e-chain on a locally compact space with the unique stationary distribution such that the strong law of large numbers does not hold. This answers negatively the question asked by \"O. Stenflo.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Stochastic processes and statistical mechanics · advanced mathematical theories