相关论文: Superprocesses with Coalescing Brownian Spatial Mo…
We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching…
We consider a superprocess with coalescing Brownian spatial motion. We first prove a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms…
A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law…
A superprocess with dependent spatial motion and interactive immigration is constructed as the pathwise unique solution of a stochastic integral equation carried by a stochastic flow and driven by Poisson processes of one-dimensional…
We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…
In this paper we obtain scaling limits of $\Lambda$-coalescents near time zero under a regularly varying assumption. In particular this covers the case of Kingman's coalescent and beta coalescents. The limiting processes are coalescents…
We show the existence of superprocesses in a random medium with location dependent branching. Technically, we make use of a duality relation to establish the uniqueness of the martingale problem and to obtain the moment formulas.
We prove a convergence theorem for a sequence of super-Brownian motions moving among hard Poissonian obstacles, when the intensity of the obstacles grows to infinity but their diameters shrink to zero in an appropriate manner. The…
We construct a family of processes, from a single Poisson process, that converges in law to a complex Brownian motion. Moreover, we find realizations of these processes that converge almost surely to the complex Brownian motion, uniformly…
A system of mutually interacting superprocesses with migration is constructed as the limit of a sequence of branching particle systems arising from population models. The uniqueness in law of the superprocesses is established using the…
A super-Brownian motion in two and three dimensions is constructed where "particles" give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based on Albeverio et al. (1995) who calculated…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
Recently Ren et al. [Stoch. Proc. Appl., 137 (2021)] have proved that the extremal process of the super-Brownian motion converges in distribution in the limit of large times. Their techniques rely heavily on the study of the convergence of…
As a first step toward a characterization of the limiting extremal process of branching Brownian motion, we proved in a recent work [Comm. Pure Appl. Math. 64 (2011) 1647-1676] that, in the limit of large time $t$, extremal particles…
We prove that the extremal process of branching Brownian motion, in the limit of large times, converges weakly to a cluster point process. The limiting process is a (randomly shifted) Poisson cluster process, where the positions of the…
We investigate the saturation regime of the condensing symmetric inclusion process on the discrete one-dimensional torus in the thermodynamical limit. In this regime, the total mass concentrates on a finite number of sites, forming…
We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian…
The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a…
We analyze the decoherence of a particle's spatial superposition moving along a stationary worldline through the Minkowski vacuum. The particle is modeled via an internal degree of freedom that couples to a scalar field, and an external…
We focus on the existence and its characterization of limit for a certain critical branching random walks in time-space random environment in 1 dimension which was introduced by Birkner et.al. Each particle performs simple random walk on…