Related papers: The cut-and-paste process

The transition law of every exchangeable Feller process on the space of countable graphs is determined by a $\sigma$-finite measure on the space of $\{0,1\}\times\{0,1\}$-valued arrays. In discrete-time, this characterization amounts to a…

Every exchangeable Feller process taking values in a suitably nice combinatorial state space can be constructed by a system of iterated random Lipschitz functions. In discrete time, the construction proceeds by iterated application of…

We study a class of Piecewise Deterministic Markov Processes with state space Rd x E where E is a finite set. The continuous component evolves according to a smooth vector field that is switched at the jump times of the discrete coordinate.…

Consider a spectrally positive Stable($1+\alpha$) process whose jumps we interpret as lifetimes of individuals. We mark the jumps by continuous excursions assigning "sizes" varying during the lifetime. As for Crump-Mode-Jagers processes…

A class of Fleming-Viot processes with decaying sampling rates and $\alpha$-stable motions that correspond to distributions with growing populations are introduced and analyzed. Almost sure long-time scaling limits for these processes are…

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In…

We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…

A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is…

We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…

A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We…

We call a random point measure infinitely ramified if for every $n\in \mathbb N$, it has the same distribution as the $n$-th generation of some branching random walk. On the other hand, branching L\'evy processes model the evolution of a…

We consider an exclusion process with long jumps in the box $\Lambda\_N=\{1, \ldots,N-1\}$, for $N \ge 2$, in contact with infinitely extended reservoirs on its left and on its right. The jump rate is described by a transition probability…

We consider piecewise deterministic Markov processes with degenerate transition kernels of the "house-of-cards"-type. We use a splitting scheme based on jump times to prove the absolute continuity, as well as some regularity, of the…

Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than a decade. One of the most well-known and widely studied problems is that of estimation of the quadratic…

We characterize various forms of positive dependence, such as association, positive supermodular association and dependence, and positive orthant dependence, for jump-Feller processes. Such jump processes can be studied through their…

The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space $\Gamma$ the evolution of which is…

Combinatorial Levy processes evolve on general state spaces of countable combinatorial structures. In this setting, the usual Levy process properties of stationary, independent increments are defined in an unconventional way in terms of the…

We study a class of interacting particle systems on $\mathbb{R}$ with two types. Particles evolve by independent jumps sampled from a fixed distribution, with type-dependent jump rates $v_+$, $v_-$ and stochastic type switching driven by…

The decomposable branching processes are relatively less studied objects, particularly in the continuous time framework. In this paper, we consider various variants of decomposable continuous time branching processes. As usual practice in…