相关论文: Equilibrium for fragmentation with immigration

The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson ran- dom measures. Some criteria for the regularity, recurrence, ergodicity and strong…

This article studies the stability of solutions of equilibrium equations arising in so-called resource dependent branching processes. We argue that these new models, building on the model already presented by Bruss (1984 a), refined and…

In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with…

In this paper, we proposed a stochastic model which describes two species of particles moving in counterflow. The model generalizes the theoretical framework describing the transport in random systems since particles can work as mobile…

In this paper we study explicit strong solutions for two difference-differential fractional equations, defined via the generator of an immigration-death process, by using spectral methods. Moreover, we give a stochastic representation of…

We consider a continuous-time symmetric branching random walk on multidimensional lattices with immigration and infinite number of initial particles. We assume that at every lattice point a process of birth and death of particles is…

We consider a spatial branching process with emigration in which children either remain at the same site as their parents or migrate to new locations and then found their own colonies. We are interested in asymptotics of the partition of…

We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We…

We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

We investigate the profound relation between the equations of biological evolution and quantum mechanics by writing a biologically inspired equation for the stochastic dynamics of an ensemble of particles. Interesting behavior is observed…

Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle…

We study systems of particles on a line which have a maximum, are locally finite and evolve with independent increments. ``Quasi-stationary states'' are defined as probability measures, on the \sigma-algebra generated by the gap variables,…

Stationary stochastic processes with independent increments, of which the Poisson process is a prominent example, are widely used to describe real world events. With the basic assumption that a counting process is stationary and has…

We consider the stochastic ranking process with the jump times of the particles determined by Poisson random measures. We prove that the joint empirical distribution of scaled position and intensity measure converges almost surely in the…

We prove the existence and pathwise uniqueness of the solution to a stochastic integral equation driven by Poisson random measures based on Kuznetsov measures for a continuous-state branching process. That gives a direct construction of the…

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains…

Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…

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 describe all countable particle systems on $\mathbb{R}$ which have the following three properties: independence, Gaussianity and stationarity. More precisely, we consider particles on the real line starting at the points of a Poisson…