Related papers: Stochastic diffusion within expanding space-time
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Continuous-time stochastic processes play an important role in the description of random phenomena, it is therefore of prime interest to study particular variables depending on their paths, like stopping time for example. One approach…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
The stochastic variational method is applied to particle systems and continuum mediums. As the brief review of this method, we first discuss the application to particle Lagrangians and derive a diffusion-type equation and the…
We study the following Cauchy problem for the linear wave equation with both time-dependent friction and time-dependent viscoelastic damping: \begin{equation} \label{EqAbstract}\tag{$\ast$} \begin{cases} u_{tt}- \Delta u + b(t)u_t -…
In this paper, we are interested in the propagation of convexity by the strong solution to a one-dimensional Brownian stochastic differential equation with coefficients Lipschitz in the spatial variable uniformly in the time variable and in…
We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
We develop a probabilistic characterisation of trajectorial expansion rates in non-autonomous stochastic dynamical systems that can be defined over a finite time interval and used for the subsequent uncertainty quantification in Lagrangian…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
This paper is devoted to a statistical analysis of the fluctuations of velocity and acceleration produced by a random distribution of point vortices in two-dimensional turbulence. We show that the velocity probability density function…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
An individual-based model of stochastic branching is proposed and studied, in which point particles drift in $\bar{\mathds{R}}_{+}:=[0,+\infty)$ towards the origin (edge) with unit speed, where each of them splits into two particles that…
Matrix differential Riccati equations are central in filtering and optimal control theory. The purpose of this article is to develop a perturbation theory for a class of stochastic matrix Riccati diffusions. Diffusions of this type arise,…
This paper is concerned with the well-posedness and regularity of the distributional solutions for the stochastic acoustic and elastic scattering problems. We show that the regularity of the solutions depends on the regularity of both the…
We study existence of global solutions and finite time blow-up of solutions to the Cauchy problem for the porous medium equation with a variable density $\rho(x)$ and a power-like reaction term $\rho(x) u^p$ with $p>1$; this is a…