Hilbert evolution algebras and its connection with discrete-time Markov chains
Rings and Algebras
2021-10-06 v2 Functional Analysis
Probability
Abstract
Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in the context of Hilbert spaces, capable to deal with infinite-dimensional spaces. We illustrate the applicability of our approach by discussing a connection with discrete-time Markov chains with countable state space.
Cite
@article{arxiv.2012.05124,
title = {Hilbert evolution algebras and its connection with discrete-time Markov chains},
author = {Sebastian J. Vidal and Paula Cadavid and Pablo M. Rodriguez},
journal= {arXiv preprint arXiv:2012.05124},
year = {2021}
}
Comments
In this version we correct a mistake in Theorem 3.1 by adding some conditions to obtain a bounded evolution operator. Moreover, we add some examples to illustrate the connection of our results with Markov chains