相关论文: Skew Convolution Semigroups and Related Immigratio…
Under a first order moment condition on the immigration mechanism, we show that an appropriately scaled supercritical and irreducible multi-type continuous state and continuous time branching process with immigration (CBI process) converges…
The generalized Fleming-Viot processes were defined in 1999 by Donnelly and Kurtz using a particle model and by Bertoin and Le Gall in 2003 using stochastic flows of bridges. In both methods, the key argument used to characterize these…
We give upper and lower estimates of densities of convolution semigroups of probability measures under explicit assumptions on the corresponding Levy measure and the Levy--Khinchin exponent. We obtain also estimates of derivatives of…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
The asymptotic normality of conditional least squares estimators for the offspring variance in critical branching processes with non-homogeneous immigration is established, under moment assumptions on both reproduction and immigration. The…
Let $(Z_n)$ be a supercritical branching process with immigration in a random environment. The small positive values and some lower deviation inequalities for $Z$ are investigated. Based on these results, the central limit theorem of $\log…
This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…
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…
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…
In many biophysical systems, key events are triggered when the fastest of many random searchers find a target. Most mathematical models of such systems assume that all searchers are initially present in the search domain, which permits the…
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…
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…
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any L\'evy process without negative jumps. Unlike the CBIs, these newly…
Many applications in medical statistics as well as in other fields can be described by transitions between multiple states (e.g. from health to disease) experienced by individuals over time. In this context, multi-state models are a popular…
In this paper, a critical Galton-Watson branching process with immigration $Z_{n}$ is studied. We first obtain the convergence rate of the harmonic moment of $Z_{n}$. Then the large deviation of $S_{Z_n}:=\sum_{i=1}^{Z_n} X_i$ is obtained,…
Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a…
Migration phenomena and all the related issues, like integration of different social groups, are intrinsically complex problems since they strongly depend on several competitive mechanisms as economic factors, cultural differences and many…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
Functional limit theorems are established for continuous-state branching processes with immigration (CBIs), where the reproduction laws have finite first moments and the immigration laws exhibit large tails. Different regimes of immigration…
Coalescents with multiple collisions (also called Lambda-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with…