TY - JOUR
AU - Akinola Yussuff Akinyele
AU - Omotoni Ezekiel Jimoh
AU - Jude Babatunde Omosowon
AU - Kareem Akanbi Bello
PY - 2022/06/02
Y2 - 2022/08/07
TI - Results of Semigroup of Linear Operator Generating a Continuous Time Markov Semigroup
JF - Earthline Journal of Mathematical Sciences
JA - EJMS
VL - 10
IS - 1
SE - Articles
DO - 10.34198/ejms.10122.97108
UR - https://earthlinepublishers.com/index.php/ejms/article/view/526
AB - 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 $y\in X$.
ER -