Related papers: Relative frequencies in multitype branching proces…
A multi-type branching process is defined as a random tree with labeled vertices, where each vertex produces offspring independently according to the same multivariate probability distribution. We demonstrate that in realizations of the…
We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the one-dimensional situation, to the strongly subcritical case.…
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…
We consider the long-term behaviour of critical multitype branching processes conditioned on non-extinction, both with respect to the forward and the ancestral processes. Forward in time, we prove a functional limit theorem in the space of…
Consider a continuous-time binary branching process conditioned to have population size n at some time t, and with a chance p for recording each extinct individual in the process. Within the family tree of this process, we consider the…
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…
Log-normal continuous random cascades form a class of multifractal processes that has already been successfully used in various fields. Several statistical issues related to this model are studied. We first make a quick but extensive review…
Strongly consistent estimates are shown, via relative frequency, for the probability of "white balls" inside a dichotomous urn when such a probability is an arbitrary continuous time dependent function over a bounded time interval. The…
We consider a multitype branching process with immigration in a random environment introduced by Key in [Ann. Probab. 15 (1987) 344--353]. It was shown by Key that, under the assumptions made in [Ann. Probab. 15 (1987) 344--353], the…
We consider a general branching population where the lifetimes of individuals are i.i.d.\ with arbitrary distribution and where each individual gives birth to new individuals at Poisson times independently from each other. In addition, we…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
Ancestral inference for branching processes in random environments involves determining the ancestor distribution parameters using the population sizes of descendant generations. In this paper, we introduce a new methodology for ancestral…
When two (possibly different in distribution) continuous-state branching processes with immigration are present, we study the relative frequency of one of them when the total mass is forced to be constant at a dense set of times. This leads…
The forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
In the multitype contact process, vertices of a graph can be empty or occupied by a type 1 or a type 2 individual; an individual of type $i$ dies with rate 1 and sends a descendant to a neighboring empty site with rate $\lambda_i$. We study…
Branching processes in a varying environment encompass a wide range of stochastic demographic models, and their complete understanding in terms of limit behaviour poses a formidable research challenge. In this paper, we conduct a thorough…
Using the annealed approach we investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in i.i.d. random environment. We show under rather general assumptions on the form of the…
Under a fourth order moment condition on the branching and a second order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous state and continuous…