相关论文: Theoretical analysis of a discrete population bala…
We study the evolution of the probability density of an asexual, one locus population under natural selection and random evolution. This evolution is governed by a Fokker-Planck equation with degenerate coefficients on the boundaries,…
Understanding the conditions ensuring the persistence of a population is an issue of primary importance in population biology. The first theoretical approach to the problem dates back to the 50's with the KiSS (after Kierstead, Slobodkin…
One of the outstanding problems of the dynamical evolution of the outer solar system concerns the observed population ratio between the Oort Cloud (OC) and the Scattered Disc (SD): observations suggest that this ratio lies between 100 and…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…
The general model of coagulation is considered. For basic classes of unbounded coagulation kernels the central limit theorem (CLT) is obtained for the fluctuations around the dynamic law of large numbers (LLN). A rather precise rate of…
Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…
In this paper, existence and uniqueness of solutions to a non-linear, initial value problem is studied. In particular, we consider a special type of problem which physically represents the time evolution of particle number density resulted…
In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernels and measure initial value, where the kernel can be Newton…
We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we…
This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…
In this paper, we propose an algorithm for estimating the parameters of a time-homogeneous hidden Markov model from aggregate observations. This problem arises when only the population level counts of the number of individuals at each time…
We introduce a new model of the evolution of the concentration of dark matter halos, c(t). For individual halos, our model approximates c(t) as a power law with a time-dependent index, such that at early times, concentration has a nearly…
This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…
Capture-recapture methods aim to estimate the size of a closed population on the basis of multiple incomplete enumerations of individuals. In many applications, the individual probability of being recorded is heterogeneous in the…
We study a crowd model proposed by R. Hughes and we describe a numerical approach to solve it. The Hughes model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori…
New explicit exponential stability conditions are presented for the non-autonomous scalar linear functional differential equation $$ \dot{x}(t)+ \sum_{k=1}^m a_k(t)x(h_k(t))+\int_{g(t)}^t K(t,s) x(s)ds=0, $$ where $h_k(t)\leq t$, $g(t)\leq…
We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed methodology amounts to a combination of sparse recovery…
The global existence of mass-conserving weak solutions to the Safronov-Dubovskii coagulation equation is shown for the coagulation kernels satisfying the at most linear growth for large sizes. In contrast to previous works, the proof mainly…