Results of Semigroup of Linear Operator Generating a Continuous Time Markov Semigroup

  • Akinola Yussuff Akinyele Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • Omotoni Ezekiel Jimoh Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • Jude Babatunde Omosowon Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • Kareem Akanbi Bello Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Keywords: $\omega$-$OCP_n$, irreducible operator, $C_0$-semigroup, Markov semigroup

Abstract

In this paper, we present results of $\omega$-order preserving partial contraction mapping creating a continuous time Markov semigroup. We use Markov and irreducible operators and their integer powers to describe the evolution of a random system whose state changes at integer times, or whose state is only inspected at integer times. We concluded that a linear operator $P:\ell^{1}(X_+)\rightarrow \ell^{1}(X_+)$ is a Markov operator if its matrix satisfies $P_{x,y}\geqslant 0$ and $\sum_{x\in X_+}P_{x,y=1}$ for all $y\in X$.

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Published
2022-06-02
How to Cite
Akinyele, A. Y., Jimoh, O. E., Omosowon, J. B., & Bello, K. A. (2022). Results of Semigroup of Linear Operator Generating a Continuous Time Markov Semigroup. Earthline Journal of Mathematical Sciences, 10(1), 97-108. https://doi.org/10.34198/ejms.10122.97108
Section
Articles