Related papers: The Moran model with random resampling rates

Let $\bX=\{X_n\}_{n\geq 1}$ and $\bY=\{Y_n\}_{n\geq 1}$ be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized sums $$ \psi_n(\bX,\bY)=\sum_{i=1}^nX_iY_i/V_n,\quad…

Sequential importance sampling algorithms have been defined to estimate likelihoods in models of ancestral population processes. However, these algorithms are based on features of the models with constant population size, and become…

We find the asymptotic distribution of the sample autocovariances of long-memory processes in cases of finite and infinite fourth moment. Depending on the interplay of assumptions on moments and the intensity of dependence, there are three…

We discuss some applications of the Mittag-Leffler function and related probability distributions in the theory of renewal processes and continuous time random walks. In particular we show the asymptotic (long time) equivalence of a generic…

We study a population model of fixed size undergoing strong selection where individuals accumulate beneficial mutations, namely the Moran model with selection. In a specific setting with strong selection, Schweinsberg showed that the…

The aim of this paper is to study the large population limit of a binary branching particle system with Moran type interactions: we introduce a new model where particles evolve, reproduce and die independently and, with a probability that…

We consider an infinite-dimensional stochastic clustering model on $\mathbb{R}$. In discrete time, each point of a unit-intensity simple point process moves halfway toward either of its left or right neighbors, chosen uniformly at random.…

We study generalized bootstrap confidence regions for the mean of a random vector whose coordinates have an unknown dependency structure. The random vector is supposed to be either Gaussian or to have a symmetric and bounded distribution.…

Evolutionary graph theory studies the evolutionary dynamics in a population structure given as a connected graph. Each node of the graph represents an individual of the population, and edges determine how offspring are placed. We consider…

Many mathematical models of evolution assume that all individuals experience the same environment. Here, we study the Moran process in heterogeneous environments. The population is of finite size with two competing types, which are exposed…

We define the Sampled Moran Genealogy Process, a continuous-time Markov process on the space of genealogies with the demography of the classical Moran process, sampled through time. To do so, we begin by defining the Moran Genealogy Process…

This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (B. Math. Biol. 66(6): 1621--1644, 2004). Their classification is based on whether each strategy…

We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise…

This paper introduces a run-and-tumble model with self-reinforcing directionality and rests. We derive a single governing hyperbolic partial differential equation for the probability density of random walk position, from which we obtain the…

We propose a Likelihood Matching approach for training diffusion models by first establishing an equivalence between the likelihood of the target data distribution and a likelihood along the sample path of the reverse diffusion. To…

We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…

The transition distribution of a sample taken from a Wright-Fisher diffusion with general small mutation rates is found using a coalescent approach. The approximation is equivalent to having at most one mutation in the coalescent tree of…

We consider consistent particle systems, which include independent random walkers, the symmetric exclusion and inclusion processes, as well as the dual of the KMP model. Consistent systems are such that the distribution obtained by first…

Given any closed Riemannian manifold $M$, we construct a reversible diffusion process on the space ${\mathcal P}(M)$ of probability measures on $M$ that is (i) reversible w.r.t.~the entropic measure ${\mathbb P}^\beta$ on ${\mathcal P}(M)$,…

For a $d$-dimensional stochastic process $(S_n)_{n=0}^N$ we obtain criteria for the existence of an equivalent martingale measure, whose density $z$, up to a normalizing constant, is bounded from below by a given random variable $f$. We…