Given a strongly local Dirichlet space and λ⩾ 0, we introduce a new notion of λ-
subharmonicity for L loc 1-functions, which we call local λ-shift defectivity, and which turns …

The aim of this note is to show, by providing an elementary way to construct
counterexamples, that the strong Feller and the joint (space-time) continuity for a semigroup …

We consider the stationary states of a chain of n anharmonic coupled oscillators, whose
deterministic Hamiltonian dynamics is perturbed by random independent sign change of the …

This paper establishes explicit solutions for fractional diffusion problems on bounded
domains. It also gives stochastic solutions, in terms of Markov processes time‐changed by …

We introduce a class of one-dimensional deterministic models of energy–volume conserving
interfaces. Numerical simulations show that these dynamics are genuinely super-diffusive …

We present sufficient conditions for the transience and the existence of local times of a Feller
process, and the ultracontractivity of the associated Feller semigroup; these conditions are …

Up to now, the nonparametric analysis of multidimensional continuous-time Markov
processes has focussed strongly on specific model choices, mostly related to symmetry of …

A maximal inequality is an inequality which involves the (absolute) supremum sup s⩽ t| X s|
or the running maximum sup s⩽ t X s of a stochastic process (X t) t⩾ 0. We discuss maximal …

The aim of this paper is to derive a stochastic representation of the solution to a nonlocal-in-
time evolution equation (with a historical initial condition), which serves a bridge between …

We study the stochastic differential equation d X t= A (X t−) d Z t, X 0= x, where Z t=(Z t (1),…,
Z t (d)) T and Z t (1),…, Z t (d) are independent one-dimensional Lévy processes with …