Search results for "92D25"
showing 3 items of 3 documents
A nonstationary cylinder-based model describing group dispersal in a fragmented habitat
2014
International audience; A doubly nonstationary cylinder-based model is built to describe the dispersal of a population from a point source. In this model, each cylinder represents a fraction of the population, i.e., a group. Two contexts are considered: The dispersal can occur in a uniform habitat or in a fragmented habitat described by a conditional Boolean model. After the construction of the models, we investigate their properties: the first and second order moments, the probability that the population vanishes, and the distribution of the spatial extent of the population.
A PHASE TRANSITION FOR LARGE VALUES OF BIFURCATING AUTOREGRESSIVE MODELS
2019
We describe the asymptotic behavior of the number $$Z_n[a_n,\infty )$$ of individuals with a large value in a stable bifurcating autoregressive process, where $$a_n\rightarrow \infty $$ . The study of the associated first moment is equivalent to the annealed large deviation problem of an autoregressive process in a random environment. The trajectorial behavior of $$Z_n[a_n,\infty )$$ is obtained by the study of the ancestral paths corresponding to the large deviation event together with the environment of the process. This study of large deviations of autoregressive processes in random environment is of independent interest and achieved first. The estimates for bifurcating autoregressive pr…
Identifiability problem for recovering the mortality rate in an age-structured population dynamics model
2014
In this article is studied the identifiability of the age-dependent mortality rate of the Von Foerster–Mc Kendrick model, from the observation of a given age group of the population. In the case where there is no renewal for the population, translated by an additional homogeneous boundary condition to the Von Foerster equation, we give a necessary and sufficient condition on the initial density that ensures the mortality rate identifiability. In the inhomogeneous case, modelled by a non-local boundary condition, we make explicit a sufficient condition for the identifiability property, and give a condition for which the identifiability problem is ill-posed. We illustrate this latter case wit…