This paper deals with ergodic theorems for particular time-inhomogeneous Markov processes, whose time-inhomogeneity is asymptotically periodic. Under a Lyapunov/minorization condition, it is shown that, for any measurable bounded function f, the time…
We study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of order . The corresponding equation turns out to have a unique solution that, depending on a particular shape of the drift, either stays above som…
We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function, which is a function of its weight and degree, and connec…
We study a general model of recursive trees where vertices are equipped with independent weights and at each time-step a vertex is sampled with probability proportional to its fitness function, which is a function of its weight and degree, and connec…
We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains
(
) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional ga…
We consider a dual risk model with constant expense rate and i.i.d. exponentially distributed gains
(
) that arrive according to a renewal process with general interarrival times. We add to this classical dual risk model the proportional ga…
Suppose that m drivers each choose a preferred parking space in a linear car park with n spots. In order, each driver goes to their chosen spot and parks there if possible, and otherwise takes the next available spot if it exists. If all drivers park s…
Given a spectrally negative Lévy process, we predict, in an
sense, the last passage time of the process below zero before an independent exponential time. This optimal prediction problem generalises [2], where the infinite-horizon problem is so…