Related papers: Conditioning subordinators embedded in Markov proc…
This note provides a simple sufficient condition ensuring that solutions of stochastic delay differential equations (SDDEs) driven by subordinators are non-negative. While, to the best of our knowledge, no simple non-negativity conditions…
We prove that the upward ladder height subordinator $H$ associated to a real valued L\'{e}vy process $\xi$ has Laplace exponent $\phi$ that varies regularly at $\infty$ (resp. at 0) if and only if the underlying L\'{e}vy process $\xi$…
This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in…
We consider a supercritical branching L\'evy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit theorem on the empirical mean position.
This papers deals with the constrained discounted control of piecewise deterministic Markov process (PDMPs) in general Borel spaces. The control variable acts on the jump rate and transition measure, and the goal is to minimize the total…
We consider a stochastic delay differential equation driven by a general Levy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is…
In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Levy process. Our approach requires to establish a…
We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…
We consider the Markov process defined by some pseudo-differential operator of the order $1<\alpha<2$ as the process generator. Using a pseudo-gradient operator, that is, the operator defined by the symbol $i\lambda|\lambda|^{\beta-1}$ with…
Two different ways of trimming the sample path of a stochastic process in D[0, 1]: global ("trim as you go") trimming and record time ("lookback") trimming are analysed to find conditions for the corresponding operators to be continuous…
This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in…
We construct optimal Markov couplings of L\'{e}vy processes, whose L\'evy (jump) measure has an absolutely continuous component. The construction is based on properties of subordinate Brownian motions and the coupling of Brownian motions by…
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…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
Consider a sequence (Z_n,Z_n^M) of bivariate L\'evy processes, such that Z_n is a spectrally positive L\'evy process with finite variation, and Z_n^M is the counting process of marks in {0,1} carried by the jumps of Z_n. The study of these…
We prove several results on the behavior near t=0 of $Y_t^{-t}$ for certain $(0,\infty)$-valued stochastic processes $(Y_t)_{t>0}$. In particular, we show for L\'{e}vy subordinators that the Pareto law on $[1,\infty)$ is the only possible…
In phenomenological applications the time evolution of subsystems immersed in an external environment are sometimes described by Markovian semigroups of Redfield type that result non-positive: the appearence of negative probabilities is…
The first step to study lower bounds for a stochastic process is to prove a special property - Sudakov minoration. The property means that if a certain number of points from the index set are well separated then we can provide an optimal…
We extend the idea of tempering stable Levy processes to tempering more general classes of Levy processes. We show that the original process can be decomposed into the sum of the tempered process and an independent point process of large…
Two kinds of conditionings for one-dimensional stable L\'evy processes are discussed via $ h $-transforms of excursion measures: One is to stay positive, and the other is to avoid the origin.