Hilbert evolution algebras and its connection with discrete-time Markov chains

Sebastian J. Vidal (), Paula Cadavid () and Pablo M. Rodriguez ()
Additional contact information
Sebastian J. Vidal: Universidad Nacional de la Patagonia “San Juan Bosco”
Paula Cadavid: Universidade Federal do ABC
Pablo M. Rodriguez: Universidade Federal de Pernambuco

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 3, 883-894

Abstract: Abstract Evolution algebras are non-associative algebras. In this work we provide an extension of this class of algebras, in a framework of Hilbert spaces, and illustrate the applicability of our approach by discussing a connection with discrete-time Markov chains with infinite countable state space. Specifically, if we associate to each possible state of such a Markov process a generator of the Hilbert evolution algebra structure, then the whole dynamics of the process can be described through consecutive applications of the evolution operator, provided certain boundedness conditions on the transition probabilities hold.

Keywords: Genetic Algebra; Evolution Algebra; Hilbert Space; Markov Chain; 17D92; 46C99; 60J10 (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-022-00304-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:54:y:2023:i:3:d:10.1007_s13226-022-00304-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-022-00304-y

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().