Starting from the forward and backward infinitesimal generators of bilateral, timehomogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schrödinger equations are first introduced by means of suitable Doob transformations. Then, by broadening with the aid of the Dirichlet forms, the results of the Nelson stochastic mechanics, we prove that it is possible to associate bil...

Introduction. An interesting but apparently neglected generalization due to Doob [l], of the ergodic theorem, is the generalization to transformations which are not necessarily one-to-one. In his paper [l], Doob showed that the transformation of the interval [0, l] into itself given by/(x) =nx (modulo 1), where n — 1 is a positive integer, is ergodic under Lebesgue measure and that the law of l...

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or switching rates are space-dependent. A long dynamical trajectory can be then analyzed via large deviations at Level 2.5 for joint probability of empirical densities, spatial currents and flows. The 2 densities alone derived optimization over More generally, an...

Let M be the Doob maximal operator on a filtered measure space and let v an Ap weight with 1<p<+∞. We try proving that ∥Mf∥Lp(v)≤p′[v]Ap1p−1∥f∥Lp(v), where 1/p+1/p′=1. Although we do not find approach which gives constant p′, obtain ∥Mf∥Lp(v)≤p1p−1p′[v]Ap1p−1∥f∥Lp(v), limp→+∞p1p−1=1.

We define and study quaternionic stochastic areas processes associated with Brownian motions on the rank-one symmetric spaces HHn HPn. The characteristic functions of fixed-time marginals these are computed allow for explicit description their corresponding large-time limits. also obtain exact formulas semigroup densities area using a Doob transform in former case density circular Jacobi proces...

In this work we analyze self-adjoint boundary value problems on networks for Schrödinger operators, in which a part of the with Neumann condition is always considered. We first characterize when energy positive semi-definite space functions satisfying null conditions. To do this, fundamental tools are Doob transform and discrete version trace function. Then, raise eigenvalue respect to weight g...