相关论文: Extinction properties of multi-type continuous-sta…
A multitype continuous-state branching process (MCSBP) ${\rm Z}=({\rm Z}_{t})_{t\geq 0}$, is a Markov process with values in $[0,\infty)^{d}$ that satisfies the branching property. Its distribution is characterised by its branching…
In Li (2011), Example 2.2, the notion of a multi-type continuous-state branching process (MCSBP) was introduced with a finite number of types, with the countably infinite case being proposed in Kyprianou and Palau (2017). One may consider…
In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…
The main purpose of this paper is to consider the multiple birth properties for multi-type Markov branching processes. We first construct a new multi-dimensional Markov process based on the multi-type Markov branching process, which can…
We consider continuous state branching processes (CSBP) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a L\'evy process with bounded variation paths. We construct a…
In this paper, we consider $n$-type Markov branching processes with immigration and resurrection. The uniqueness criteria are first established. Then, a new method is found and the explicit expression of extinction probability is…
These notes were used in a short graduate course on branching processes the author gave in Beijing Normal University. The following main topics are covered: scaling limits of Galton--Watson processes, continuous-state branching processes,…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Under mild non-degeneracy assumptions on branching rates in each generation, we provide a criterion for almost-sure extinction of a multi-type branching process with time-dependent branching rates. We also provide a criterion for the total…
A continuous-state polynomial branching process is constructed as the pathwise unique solution of a stochastic integral equation with absorbing boundary condition. The extinction and explosion probabilities and the mean extinction and…
We consider a critical branching particle system in $\R^d$, composed of individuals of a finite number of types $i\in\{1,...,K\}$. Each individual of type $i$ moves independently according to a symmetric $\alpha_i$-stable motion. We assume…
The long-term behaviors of flows of continuous-state branching processes are characterized through subordinators and extremal processes. The extremal processes arise in the case of supercritical processes with infinite mean and of…
In this paper, we study the speed of extinction of continuous state branching processes in subcritical L\'evy environments. More precisely, when the associated L\'evy process to the environment drifts to $-\infty$ and, under a suitable…
For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population…
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…
Consider the continuous-time Markov Branching Process. In critical case we consider a situation when the generating function of intensity of transformation of particles has the infinite second moment, but its tail regularly varies in sense…
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…
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…
We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is…
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated…