A Correlation Inequality for Markov Processes in Partially Ordered State Spaces

Harris, T. E.

Harris, T. E.

Ann. Probab., Tome 5 (1977) no. 6, p. 451-454 / Harvested from Project Euclid

Résumé

Let $E$ be a finite partially ordered set and $M_p$ the set of probability measures in $E$ giving a positive correlation to each pair of increasing functions on $E$. Given a Markov process with state space $E$ whose transition operator (on functions) maps increasing functions into increasing functions, let $U_t$ be the transition operator on measures. In order that $U_tM_p \subset M_p$ for each $t \geqq 0$, it is necessary and sufficient that every jump of the sample paths is up or down.

Publié le : 1977-06-14
Classification: Correlation inequalities, partial order, Markov, 60B99, 60K35

@article{1176995804,
     author = {Harris, T. E.},
     title = {A Correlation Inequality for Markov Processes in Partially Ordered State Spaces},
     journal = {Ann. Probab.},
     volume = {5},
     number = {6},
     year = {1977},
     pages = { 451-454},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995804}
}

Harris, T. E. A Correlation Inequality for Markov Processes in Partially Ordered State Spaces. Ann. Probab., Tome 5 (1977) no. 6, pp.  451-454. http://gdmltest.u-ga.fr/item/1176995804/