Related papers: Limit theorems for renewal shot noise processes wi…

For many stochastic diffusion processes with mean field interaction, convergence of the rescaled total mass processes towards a diffusion process is known. Here we show convergence of the so-called finite system scheme for interacting…

Let $\rho$ be a borelian probability measure on $\mathrm{SL}_d(\mathbb{R})$. Consider the random walk $(X_n)$ on $\mathbb{R}^d\setminus\{0\}$ defined by $\rho$ : for any $x\in \mathbb{R}^d\setminus\{0\}$, we set $X_0 =x$ and $X_{n+1} =…

Recently, research on denoising diffusion models has expanded its application to the field of image restoration. Traditional diffusion-based image restoration methods utilize degraded images as conditional input to effectively guide the…

Zeta-function regularization is applied to evaluate the one-loop effective potential for SO(10) grand-unified theories in de Sitter cosmologies. When the Higgs scalar field belongs to the 210-dimensional irreducible representation of…

In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed…

We build and study a recursive algorithm based on the occupation measure of an Euler scheme with decreasing step for the numerical approximation of the quasistationary distribution (QSD) of an elliptic diffusion in a bounded domain. We…

It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…

Let $F\{dx\}$ be a relatively stable probability distribution on the whole real line and $S_n$ the random walk started at the origin with step distribution $F$. We obtain an exact asymptotic form of the Green measure $U\{x+dy\}=…

This paper studies high-dimensional M-estimation in the proportional asymptotic regime (p/n -> gamma > 0) when the noise distribution has infinite variance. For noise with regularly-varying tails of index alpha in (1,2), we establish that…

Let $N(\tau)$ be a renewal process for independent holding times $\{X_i\}_{k \ge 0}$ ,where $\{X_k\}_{k\ge 1}$ are identically distributed with density $p(x)$. If the associated residual time $R(\tau)$ has a density $u(x,\tau)$, its…

This paper considers sequences of points on the real line which have been randomly translated, and provides conditions under which various notions of convergence to a limiting point process are equivalent. In particular we consider…

We study the hydrodynamic behaviour of the symmetric zero-range process on the finite interval $\{1, \ldots, N-1\}$ in contact with slow reservoirs at the boundary. Particles are injected and removed at sites $1$ and $N-1$ at rates that…

The one-dimensional propagation of seismic waves with constant Q is shown to be governed by an evolution equation of fractional order in time, which interpolates the heat equation and the wave equation. The fundamental solutions for the…

The exponential upper bounds for the convergence rate of the distribution of restorable element with partially energized standby redundancy are founded, in the case when all working and repair times are bounded by exponential random…

A fractionally integrated inverse stable subordinator (FIISS) is the convolution of a power function and an inverse stable subordinator. We show that the FIISS is a scaling limit in the Skorokhod space of a renewal shot noise process with…

In many real-world dynamical systems, obtaining precise models of system uncertainty remains a challenge. It may be difficult to estimate noise distributions or robustness bounds, especially when the distributions/robustness bounds vary…

In this article, we prove a new functional limit theorem for the partial sum sequence $S_{[nt]}=\sum_{i=1}^{[nt]}X_i$ corresponding to a linear sequence of the form $X_i=\sum_{j \in \bZ}c_j \xi_{i-j}$ with i.i.d. innovations $(\xi_i)_{i \in…

We consider positive radial decreasing blow-up solutions of the semilinear heat equation \begin{equation*} u_t-\Delta u=f(u):=e^{u}L(e^{u}),\quad x\in \Omega,\ t>0, \end{equation*} where $\Omega=\mathbb{R}^n$ or $\Omega=B_R$ and $L$ is a…

We investigate Bose-Einstein condensation for interacting bosons at zero and nonzero temperature. Functional renormalization provides us with a consistent method to compute the effect of fluctuations beyond the Bogoliubov approximation. For…

We establish limit theorems involving weak convergence of multiple generations of critical and supercritical branching processes. These results arise naturally when dealing with the joint asymptotic behavior of functionals defined in terms…