In this paper, we study a reflected Markov-modulated Brownian motion with a two sided reflection in which the drift, diffusion coefficient and the two boundaries are (jointly) modulated by a finite state space irreducible continuous time Markov chain. The goal is to compute the stationary...

The aim of this paper is to compare the waiting times of customers in multiple-server queues, where the idle times are removed, with different numbers of servers. For this purpose we develop some results regarding the vector-valued marked point process whose points are arrival epochs of the...

The purpose of this note is to provide an equivalent definition and an alternative proof of uniqueness of the one-dimensional reflection map which is more a direct derivation that structurally leads to the form of the map when it exists, does not involve integration (neither in the definition...

Kella and Whitt (J. Appl. Probab. 29 (1992) 396) introduced a martingale {Mt} for processes of the form Zt=Xt+Yt where {Xt} is a Lévy process and Yt satisfies certain regularity conditions. In particular, this provides a martingale for the case where Yt=Lt where Lt is the local time at zero of...

Motivated by and with the aim of generalizing (Bar-Lev and Enis, 1987), we identify various limit laws of certain centralizing transformations of families of random variables by establishing a nontrivial equivalence with limits of their Laplace–Stieltjes transforms evaluated at transformed values.

For certain subordinators (Xt)t≥0 it is shown that the process (−tlogXts)s0 tends to an extremal process (η̂s)s0 in the sense of convergence of the finite dimensional distributions. Additionally it is also shown that (z∧(−tlogXts))s≥0 converges weakly to (z∧η̂s)s≥0 in D[0,∞),...