Related papers: On continuous state branching processes: condition…
A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the classical Lamperti law for the occupation…
We consider Markov processes in continuous time with state space $\posint^N$ and provide two sufficient conditions and one necessary condition for the existence of moments $E(\|X(t)\|^r)$ of all orders $r \in \nat$ for all $t \geq 0$. The…
Let \xi_t, t\in[0,T], be a strong Markov process with values in a complete separable metric space (X,\rho) and with transition probability function P_{s,t}(x,dy), 0\le s\le t\le T, x\in X. For any h\in[0,T] and a>0, consider the function…
Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In this paper, we show that the distribution of the absorption time is absolutely continuous with an infinitely continuously differentiable density. We…
We construct a flow of continuous time and discrete state branching processes. Some scaling limit theorems for the flow are proved, which lead to the path-valued branching processes and nonlocal branching superprocesses over the positive…
Understanding the space-time features of how a L\'evy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial…
he starting process with countable number of types \mu(t) generates a stopped branching process \xi(t). The starting process stops, by falling into the nonempty set S. It is assumed, that the starting process is subcritical, indecomposable…
Dilative semistability extends the notion of semi-selfsimilarity for infinitely divisible stochastic processes by introducing an additional scaling in the convolution exponent. It is shown that this scaling relation is a natural extension…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
The Lamperti transform offers a powerful bridge between self-similar processes and stationary dynamics, making it especially useful for analyzing anomalous diffusion models that lack stationary increments. In this paper we examine the…
We prove that the class of discrete time stationary max-stable process satisfying the Markov property is equal, up to time reversal, to the class of stationary max-autoregressive processes of order $1$. A similar statement is also proved…
A new sufficient condition is proved for the existence of stochastic semigroups generated by the sum of two unbounded operators. It is applied to one-dimensional piecewise deterministic Markov processes, where we also discuss the existence…
We study the long time behaviour of a Markov process evolving in $\mathbb{N}$ and conditioned not to hit 0. Assuming that the process comes back quickly from infinity, we prove that the process admits a unique quasi-stationary distribution…
Taking account of recent developments in the representation of $d$-dimensional isotropic stable L\'evy processes as self-similar Markov processes, we consider a number of new ways to condition its path. Suppose that $\Omega$ is a region of…
Consider a Lamperti-Kiu Markov additive process $(J_t,\xi_t:t\geq0)$ on $\{+,-\}\times\mathbb{R}\cup\infty$ where $J$ is the modulating Markov chain component. First, we study the finiteness of the exponential functional and then consider…
The aim of this paper is to prove stability of traveling waves for integro-differential equations connected with branching Markov processes. In other words, the limiting law of the left-most particle of a (time-continuous) branching Markov…
Using Monte Carlo simulations we have studied the transition from an "active" steady state to an absorbing "inactive" state for two versions of the branching annihilating random walks with parity conservation on a square lattice. In the…
It is well known that under some conditions the almost sure survival probability of a multitype branching processes in random environment is positive if the Lyapunov exponent corresponding to the expectation matrices is positive, and zero…
Suppose that $(X_t)_{t \ge 0}$ is a one-dimensional Brownian motion with negative drift $-\mu$. It is possible to make sense of conditioning this process to be in the state $0$ at an independent exponential random time and if we kill the…
We characterize all possible independent symmetric alpha-stable (SaS) components of an SaS process, 0<alpha<2. In particular, we focus on stationary SaS processes and their independent stationary SaS components. We also develop a parallel…