ﻻ يوجد ملخص باللغة العربية
We examine in this article the one-dimensional, non-local, singular SPDE begin{equation*} partial_t u ;=; -, (-Delta)^{1/2} u ,-, sinh(gamma u) ,+, xi;, end{equation*} where $gammain mathbb{R}$, $(-Delta)^{1/2}$ is the fractional Laplacian of order $1/2$, $xi$ the space-time white noise in $mathbb{R} times mathbb{T}$, and $mathbb{T}$ the one-dimensional torus. We show that for $0<gamma^2<pi/7$ the Da Prato--Debussche method applies. One of the main difficulties lies in the derivation of a Schauder estimate for the semi-group associated to the fractional Laplacian due to the lack of smoothness resulting from the long range interaction.
We introduce the $Ntimes N$ random matrices $$ X_{j,k}=expleft(2pi i sum_{q=1}^d omega_{j,q} k^qright) quad text{with } {omega_{j,q}}_{substack{1leq jleq N 1leq qleq d}} text{ i.i.d. random variables}, $$ and $d$ a fixed integer. We prove that the di
General theorems on the closability and quasi-regularity of non-local Markovian symmetric forms on probability spaces $(S, {cal B}(S), mu)$, with $S$ Fr{e}chet spaces such that $S subset {mathbb R}^{mathbb N}$, ${cal B}(S)$ is the Borel $sigma$-field
Consider a one-dimensional stepping stone model with colonies of size $M$ and per-generation migration probability $ u$, or a voter model on $mathbb{Z}$ in which interactions occur over a distance of order $K$. Sample one individual at the origin and
A many-server queueing system is considered in which customers with independent and identically distributed service times enter service in the order of arrival. The state of the system is represented by a process that describes the total number of cu
We investigate the emergence of singular solutions in a non-local model for a magnetic system. We study a modified Gilbert-type equation for the magnetization vector and find that the evolution depends strongly on the length scales of the non-local e