Related papers: Agmon-type estimates for a class of jump processes

In this paper, for a family of second-order elliptic equations with rapidly oscillating periodic coefficients and rapidly oscillating periodic potentials, we are interested in the $H^1$ convergence rates and the Dirichlet eigenvalues and…

We show the existence of a broad class of affine Markov processes in the cone of positive self-adjoint Hilbert-Schmidt operators. Such processes are well-suited as infinite dimensional stochastic volatility models. The class of processes we…

The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating…

Let $E$ be a locally compact separable metric space and $m$ be a positive Radon measure on it. Given a nonnegative function $k$ defined on $E\times E$ off the diagonal whose anti-symmetric part is assumed to be less singular than the…

In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these…

We propose a general approach for quantitative convergence analysis of non-reversible Markov processes, based on the concept of second-order lifts and a variational approach to hypocoercivity. To this end, we introduce the flow Poincar{\'e}…

We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…

We aim at estimating the invariant density associated to a stochastic differential equation with jumps in low dimension, which is for $d=1$ and $d=2$. We consider a class of jump diffusion processes whose invariant density belongs to some…

This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only…

The paper considers a continuous-time birth-death process where the jump rate has an asymptotically polynomial dependence on the process position. We obtain a rough exponential asymptotics for the probability of excursions of a re-scaled…

This work is concerned with the gradient flow of absolutely $p$-homogeneous convex functionals on a Hilbert space, which we show to exhibit finite ($p<2$) or infinite extinction time ($p \geq 2$). We give upper bounds for the finite…

We investigate the Poisson regression method for Markov and semi-Markov jump processes from a nonparametric angle, allowing the lengths of the time and duration intervals in the partition to vary with the number of observations. Imposing no…

We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on $\R^d$. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying…

The large deviations at various levels that are explicit for Markov jump processes satisfying detailed-balance are revisited in terms of the supersymmetric quantum Hamiltonian $H$ that can be obtained from the Markov generator via a…

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

A compound Poisson process whose parameters are all unknown is observed at finitely many equispaced times. Nonparametric estimators of the jump and L\'evy distributions are proposed and functional central limit theorems using the uniform…

We study nonlocal operators acting on functions in the Euclidean space. The operators under consideration generate anisotropic jump processes, e.g., a jump process that behaves like a stable process in each direction but with a different…

We study the iteration of the process "a particle jumps to the right" in permutations. We prove that the set of permutations obtained in this model after a given number of iterations from the identity is a class of pattern avoiding…

We study the large deviation behaviour of the trajectories of empirical distributions of independent copies of time-homogeneous Feller processes on locally compact metric spaces. Under the condition that we can find a suitable core for the…

The goal of this paper is to establish sharp two-sided estimates on the heat kernels of two types of purely discontinuous symmetric Markov processes in the upper half-space of $\mathbb R^d$ with jump kernels degenerate at the boundary. The…