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...

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,∞),...

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.

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...

Two-sided reflected Markov-modulated Brownian motion with applications to fluid queues and dividend payouts

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...

In this paper we consider the first passage process of a spectrally negative Markov additive process (MAP). The law of this process is uniquely characterized by a certain matrix function, which plays a crucial role in fluctuation theory. We show how to identify this matrix using the theory of...

In this paper we consider the two-sided reflection of a Markov modulated Brownian motion by analyzing the spectral properties of the matrix polynomial associated with the generator of the free process. We show how to compute for the general case the Laplace transform of the stationary...