Topics in Markov Additive Processes.
Many complex systems occurring in various application share the property that the underlying Markov process remains in certain regions of the state space for long times, and that transitions between such metastable sets occur only rarely. Often the dynamics within each metastable set is of minor importance, but the transitions between these sets are crucial for the behavior and the understanding of the system. Since simulations of the original process are usually prohibitively expensive, the effective...
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.
We investigate the transience/recurrence of a non-Markovian, one-dimensional diffusion process which consists of a Brownian motion with a non-anticipating drift that has two phases – a transient to mode which is activated when the diffusion is sufficiently near its running maximum, and a recurrent mode which is activated otherwise. We also consider the speed of a diffusion with a two-phase drift, where the drift is equal to a certain non-negative constant when the diffusion is sufficiently near...