相关论文: Branching Processes with Immigration in a Random E…
A special type of immigration associated with measure-valued branching processes is formulated by using skew convolution semigroups. We give characterization for a general inhomogeneous skew convolution semigroup in terms of probability…
This paper demonstrates a new regeneration processes technology making use of positive stable distributions. We study the asymptotic behavior of branching processes with a randomly controlled migration component. Using the new method, we…
Consider a critical Galton--Watson branching process with immigration, where the offspring distribution belongs to the domain of attraction of a $(1 + \alpha)$-stable law with $\alpha \in (0,1)$, and the immigration distribution either (i)…
We give sufficient conditions on the offspring, the initial and the immigration distributions under which a second-order Galton-Watson process with immigration is regularly varying.
We analyze the stationary tail of a fixed-point equation arising in branching processes with state-independent immigration, when both immigration and offspring distributions have heavy tails with boundary index one. We prove that \[ P(X >…
This is a survey on recent progresses in the study of branching processes with immigration, generalized Ornstein-Uhlenbeck processes and affine Markov processes. We mainly focus on the applications of skew convolution semigroups and the…
A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time-space noises. The family can be regarded as an inhomogeneous increasing path-valued…
We consider a stationary continuous model of random size population with non-neutral mutations using a continuous state branching process with non-homogeneous immigration. We assume the type (or mutation) of the immigrants is random given…
Continuous state branching processes with immigration are studied. We are particularly concerned with the associated (non-symmetric) Dirichlet form. After observing that gamma distributions are only reversible distributions for this class…
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 study supercritical branching processes under the influence of an i.i.d. emigration component. We provide conditions, under which the lifetime of the process is finite respectively has a finite expectation. A new version of the…
A critical branching process with immigration which evolve in a random environment is considered. Assuming that immigration is not allowed when there are no individuals in the aboriginal population we investigate the tail distribution of…
By a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. The so defined random processes generalize random processes…
A general continuous-state branching processes in random environment (CBRE-process) is defined as the strong solution of a stochastic integral equation. The environment is determined by a L\'evy process with no jump less than $-1$. We give…
This paper introduces stochastic processes that describe the evolution of systems of particles in which particles immigrate according to a Poisson measure and split according to a self-similar fragmentation. Criteria for existence and…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
By decomposing the random walk path, we construct a multitype branching process with immigration in random environment for corresponding random walk with bounded jumps in random environment. Then we give two applications of the branching…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
The paper studies a class of critical Markov branching processes with infinite variance of the offspring distribution. The processes admit also an immigration component at the jump-points of a non-homogeneous Poisson process, assuming that…
We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The…