Level-crossing ordering of semi-Markov processes and markov chains

Level-crossing Ordering of Semi-markov Processes and Markov Chains

We extend the definition of level-crossing ordering of stochastic processes, proposed by Irle andGani (2001), to the case in which the times to exceed levels are compared using an arbitrary stochastic order, and work, in particular, with integral stochastic orders closed for convolution. Using a sample-path approach, we establish level-crossing ordering results for the case in which the slower ...

The KTH Visit in Semi-Markov Processes

Level Crossing Ordering of Skip-free-to-the-right Continuous-time Markov Chains

As proposed by Irle and Gani in 2001, a process X is said to be slower in level crossing than a process Y if it takesX stochastically longer to exceed any given level than it does Y . In this paper, we extend a result of Irle (2003), relative to the level crossing ordering of uniformizable skip-free-to-the-right continuous-time Markov chains, to derive a new set of sufficient conditions for the...

Hidden hybrid Markov/semi-Markov chains

Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains for the modeling of short or medium size homogeneous zones along sequences but also enables the modeling of long zones with Markovian states. The...

Ordering Monte Carlo Markov Chains

Markov chains having the same stationary distribution can be partially ordered by performance in the central limit theorem. We say that one chain is at least as good as another in the e ciency partial ordering if the variance in the central limit theorem is at least as small for every L( ) functional of the chain. Peskun partial ordering implies e ciency partial ordering [25, 30]. Here we show ...