On the kernel of the covariance operator for Markov semigroups, I.

Abstract

We analyze the covariance operator from a Central Limit Theorem for functionals on countable ergodic Markov chains. We provide an algorithm for characterizing the covariance operator and determining its kernel. We present examples, including countable and finite Markov chains.

Keywords:

• Functionals on Markov chains
• homological equation
• Poisson equation
• loop Markov chain
• KPS chain
• limit theorems

AMS Subject Classifications:

• 60J80
• 92D25

Notes

No potential conflict of interest was reported by the authors.

1 In fact, . That is, .

Additional information

Funding

This work was supported by the University of North Carolina at Charlotte.