Related papers: Limit theorems for renewal shot noise processes wi…
We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for \[ u_t = u \Delta u + u \int_\Omega |\nabla u|^2 \] in bounded domains $\Omega\subset\mathbb{R}^n$ and prove that solutions converge to…
In previous work [cond-mat/9904207,cond-mat/9904215] we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential…
We study the asymptotic properties of the solutions of a nonlinear renewal equation. The main contribution of the present article is to provide stability and convergence results around equilibrium solutions, under some local subcritical…
In this paper, we consider a bidimensional renewal risk model with constant force of interest, in which the claim size vector with certain local subexponential marginal distribution and its inter-arrival time are subject to a new…
We consider the spatial Lambda-Fleming-Viot process model for frequencies of genetic types in a population living in R^d, with two types of individuals (0 and 1) and natural selection favouring individuals of type 1. We first prove that the…
The scaling of the exact solution of a hyperbolic balance law generates a family of scaled problems in which the source term does not depend on the current solution. These problems are used to construct a sequence of solutions whose…
We consider the empirical process G_t of a one-dimensional diffusion with finite speed measure, indexed by a collection of functions F. By the central limit theorem for diffusions, the finite-dimensional distributions of G_t converge weakly…
The objective of this dissertation is to prove a scaling limit for the exit of a domain problem of a small noise system with underlying hyperbolic dynamics. In this case, Large Deviation kind of estimates fail to provide a complete picture…
We consider a class of reaction-diffusion equations with a stochastic perturbation on the boundary. We show that in the limit of fast diffusion, one can rigorously approximate solutions of the system of PDEs with stochastic Neumann boundary…
We prove weak convergence on the Skorokhod space of Galton-Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot…
We prove several forms of renewal theorem tailored to renewal processes with marks and clusters. In particular, for an i.i.d. sequence $(\xi_i,X_i)_{i \geq 0}$, where $\xi_0$ denotes a finite point process on $\mathbb{R}$ and $X_0$ denotes…
We study the photon shot noise dephasing of a superconducting transmon qubit in the strong-dispersive limit, due to the coupling of the qubit to its readout cavity. As each random arrival or departure of a photon is expected to completely…
In this paper we study the convergence in distribution and the local limit theorem for the partial sums of linear random fields with i.i.d. innovations that have infinite second moment and belong to the domain of attraction of a stable law…
We consider a numerical approximation of a linear quadratic control problem constrained by the stochastic heat equation with non-homogeneous Neumann boundary conditions. This involves a combination of distributed and boundary control, as…
We consider subordinators $X_\alpha=(X_\alpha(t))_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator $(S_\alpha(t))_{t\ge 0}$ (where $\alpha\in(0,1)$); thus, with the property that $\overline{\Pi}_\alpha$, the tail function…
We study the explosion phenomenon of nonlinear continuous-state branching processes (nonlinear CSBPs). First an explicit integral test for explosion is designed when the rate function does not increase too fast. We then exhibit three…
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the $\ga$-stable regenerative set. We then apply these results to the strip wetting model which is a…
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes…
The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a…
In this paper we prove strong well-posedness for a system of stochastic differential equations driven by a degenerate diffusion satisfying a weak-type H\"ormander condition, assuming H\"older regularity assumptions on the drift coefficient.…