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

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. Specifi...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2023-09, Vol.54 (3), p.883-894
Main Authors: Vidal, Sebastian J., Cadavid, Paula, Rodriguez, Pablo M.
Format: Article
Language:English
Subjects:
Algebra
Applications of Mathematics
Evolution
Hilbert space
Markov chains
Mathematics
Mathematics and Statistics
Numerical Analysis
Operators (mathematics)
Original Research
Transition probabilities
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Summary: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.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-022-00304-y