Related papers: Occupation densities in solving exit problems for …
As well known, all functionals of a Markov process may be expressed in terms of the generator operator, modulo some analytic work. In the case of spectrally negative Markov processes however, it is conjectured that everything can be…
In this paper, we identify Laplace transforms of occupation times of intervals until first passage times for spectrally negative L\'evy processes. New analytical identities for scale functions are derived and therefore the results are…
Using a new approach, for spectrally negative L\'evy processes we find joint Laplace transforms involving the last exit time (from a semi-infinite interval), the value of the process at the last exit time and the associated occupation time,…
We study the classical occupancy problem from the viewpoint of its embedding Markov chain. We derive new expressions for the probability mass function and (complementary) distribution function in generalized form. Furthermore, we derive a…
Given a spectrally negative L\'evy process and independent Poisson observation times, we consider a periodic barrier strategy that pushes the process down to a certain level whenever it is above it. We also consider the versions with…
We study the scale function of the spectrally negative phase-type Levy process. Its scale function admits an analytical expression and so do a number of its fluctuation identities. Motivated by the fact that the class of phase-type…
For refracted spectrally negative L\'evy processes, we identify expressions of several quantities related to Laplace transforms on their weighted occupation times until first exit times. Such quantities are expressed in terms of unique…
We construct a Hunt process that can be described as an isotropic $\alpha$-stable L\'evy process reflected from the complement of a bounded open Lipschitz set. In fact, we introduce a new analytic method for concatenating Markov processes.…
In this paper we study a spectrally negative L\'{e}vy process that is reflected at its draw-down level whenever a draw-down time from the running supremum arrives. Using an excursion-theoretical approach, for such a reflected process we…
A new approach to solve the continuous-time stochastic inventory problem using the fluctuation theory of Levy processes is developed. This approach involves the recent developments of the scale function that is capable of expressing many…
We calculate the spectral gap of the Markov matrix of the totally asymmetric simple exclusion process (TASEP) on a ring of L sites with N particles. Our derivation is simple and self-contained and extends a previous calculation that was…
Recent fluctuation identities for $\alpha$-stable L\'evy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory…
In this work, we propose a new lecture of input-output model reconciliation Markov chain and the dominance theory, in the field of interindustrial poles interactions. A deeper lecture of Leontieff table in term of Markov chain is given,…
The analysis of many problems of interest associated with Markov chains, e.g. stationary distributions, moments of first passage time distributions and moments of occupation time random variables, involves the solution of a system of linear…
The classical and extended occupancy distributions are useful for examining the number of occupied bins in problems involving random allocation of balls to bins. We examine the extended occupancy problem by framing it as a Markov chain and…
In this paper, we study fluctuation identities for spectrally negative L\'evy processes killed by a general class of additive functionals. We consider positive co-natural additive functionals (PcNAFs), which include as special cases both…
Studying the behaviour of Markov processes at boundary points of the state space has a long history, dating back all the way to William Feller. With different motivations in mind entrance and exit questions have been explored for different…
We investigate one of the simplest multi-species generalizations of the one dimensional exclusion process with reflective boundaries. The Markov matrix governing the dynamics of the system splits into blocks (sectors) specified by the…
Model reduction of Markov processes is a basic problem in modeling state-transition systems. Motivated by the state aggregation approach rooted in control theory, we study the statistical state compression of a discrete-state Markov chain…
This paper presents a set of results relating to the occupation time $\alpha(t)$ of a process $X(\cdot)$. The first set of results concerns exact characterizations of $\alpha(t)$ for $t\geq0$, e.g., in terms of its transform up to an…