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Evolution Algebras and Markov Chains

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1921)

For a Markov chain, we can define an evolution algebra by taking states as generators and transition probability vectors as defining relations. We may say an evolution algebra defined by a Markov chain is a Markov evolution algebra. Every property of a Markov chain can be redefined by its Markov evolution algebra. In other words, properties of Markov chains can be revealed by studying their evolution algebras. Moreover, Markov chains, as a type of dynamical systems, have a hidden algebraic aspect. In first three sections of this chapter we study the relations between Markov chains and evolution algebras. In the last section, the hierarchy of a general Markov chain is revealed naturally by its evolution algebra.

Keywords

  • Markov Chain
  • Evolution Operator
  • Sojourn Time
  • Kolmogorov Equation
  • Geometric Multiplicity

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 2008 Springer-Verlag Berlin Heidelberg

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(2008). Evolution Algebras and Markov Chains. In: Evolution Algebras and their Applications. Lecture Notes in Mathematics, vol 1921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74284-5_4

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