相关论文: Limit theorems for conditioned multitype Dawson-Wa…

For a minimal diffusion process on $ (a,b) $, any possible extension of it to a standard process on $ [a,b] $ is characterized by the characteristic measures of excursions away from the boundary points $ a $ and $ b $. The generator of the…

We consider the time evolution of the supercritical Galton-Watson model of branching particles with extra parameter (mass). In the moment of the division the mass of the particle (which is growing linearly after the birth) is divided in…

We demonstrate that the correlations observed in conditioned multiplier distributions of the energy dissipation in fully developed turbulence can be understood as an unavoidable artefact of the observation procedure. Taking the latter into…

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…

We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…

This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments…

We consider a supercritical branching process $Z_n$ in a stationary and ergodic random environment $\xi =(\xi_n)_{n\ge0}$. Due to the martingale convergence theorem, it is known that the normalized population size $W_n=Z_n/ (\mathbb E…

We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…

Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here we focus on similar problems in the context of the standard…

We are concerned with the persistence of both predator and prey in a diffusive predator-prey system with a climate change effect, which is modeled by a spatial-temporal heterogeneity depending on a moving variable. Moreover, we consider…

We prove that weakly continuous solutions to martingale problems admit a canonical regular conditional probability distribution. This allows for the construction of time consistent convex dynamic procedures in a non dominated setting.…

The finite element solution of two-dimensional anisotropic diffusion problems is considered. A Delaunay-type mesh condition is developed for linear finite element approximations to satisfy a discrete maximum principle. The condition is…

A multi-type neutral Cannings population model with mutation and fixed subpopulation sizes is analyzed. Under appropriate conditions, as all subpopulation sizes tend to infinity, the ancestral process, properly time-scaled, converges to a…

We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…

We consider a marking procedure of the vertices of a tree where each vertex is marked independently from the others with a probability that depends only on its out-degree. We prove that a critical Galton-Watson tree conditioned on having a…

This note investigates core properties of martingales, emphasizing the measure-theoretic formulation of conditional expectation, the martingale transform, and the upcrossing lemma. These results lead to the Martingale Convergence Theorem,…

It is well known that upward conditioned Brownian motion is a three-dimensional Bessel process, and that a downward conditioned Bessel process is a Brownian motion. We give a simple proof for this result, which generalizes to any continuous…

A population genetics model based on a multitype branching process, or equivalently a Galton-Watson branching process for multiple alleles, is pre- sented. The diffusion limit forward Kolmogorov equation is derived for the case of neutral…

The present paper provides a characterisation of exchangeable pairs of random measures $(\widetilde\mu_1,\widetilde\mu_2)$ whose identical margins are fixed to coincide with the distribution of a gamma completely random measure, and whose…

Let $(X_t)_{t\geq 0}$ be a regular one-dimensional diffusion that models a biological population. If one assumes that the population goes extinct in finite time it is natural to study the $Q$-process associated to $(X_t)_{t\geq 0}$. This is…