Dependence in Lag for Markov Processes on Partially Ordered State Space Rafa l Kulik Wroc law University Mathematical Institute Pl. Grunwaldzki 2/4 50-384 Wroc law Poland and Department of Mathematics and Statistics University of Ottawa 585 King Edward Av. K1N 6N5 Ottawa, ON, Canada February 26, 2004 Abstract Let Y =(Y (t),t ≥ 0) be a stationary homogeneous Markov process with partially ordered state space E. In this paper we show that, under stochastic monotonicity assumptions, a dependence in this process decrease in time. Our results extend the one existing for linearly ordered case and allow us to skip an assumption about uniform semigroups. We apply our results to Jackson networks. 1 1 Introduction Let Y =(Y (t),t ≥ 0) be a stationary homogeneous Markov process with partially ordered state space E. In this paper we show that, under stochastic monotonicity assumptions, a dependence in this process decrease in time in the sense of super- modular ordering. This is counterpart to the results in totally ordered case, see 1 Key words:; AMS 2000 Subject Classification: 60K25 Short title: Dependence in Lag for Markov Processes Supported by KBN-DAAD .... matematyka/markov-partial-order/smmon-markov-partial.tex 1