Related papers: Jump processes as Generalized Gradient Flows
We discuss a special form of gradient descent that in the literature has become known as the so-called linearised Bregman iteration. The idea is to replace the classical (squared) two norm metric in the gradient descent setting with a…
We characterize various forms of positive dependence for a general class of time-inhomogeneous Markov processes called Feller evolution processes (FEPs) and for jump-FEPs. General FEPs can be studied through their time and state-space…
In this work we derive a class of geometric flow equations for metric-scalar systems. Thereafter, we construct them from some general string frame action by performing volume-preserving fields variations and writing down the associated…
We propose a moving horizon estimation scheme for joint state and parameter estimation for nonlinear uncertain discrete-time systems. We establish robust exponential convergence of the combined estimation error subject to process…
We use the distances introduced in a previous joint paper to exhibit the gradient flow structure of some drift-diffusion equations for a wide class of entropy functionals. Functional inequalities obtained by the comparison of the entropy…
A stable-like process is a Feller process $(X_t)_{t\geq 0}$ taking values in $\mathbb{R}^d$ and whose generator behaves, locally, like an $\alpha$-stable L\'evy process, but the index $\alpha$ and all other characteristics may depend on 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…
The basic concepts of classical mechanics are given in the operator form. Then, the hybrid systems approach, with the operator formulation of both quantum and classical sector, is applied to the case of an ideal nonselective measurement. It…
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 construct a non-decreasing pure jump Markov process, whose jump measure heavily depends on the values taken by the process. We determine the singularity spectrum of this process, which turns out to be random and to depend locally on the…
The evolution is described of an infinite system of hopping point particles in $\mathbb{R}^d$. The states of the system are probability measures on the space of configurations of particles. Under the condition that the initial state $\mu_0$…
We construct a large class of completely positive and trace preserving non-Markovian dynamical maps for an open quantum system. These maps arise from a piecewise dynamics characterized by a continuous time evolution interrupted by jumps,…
In this paper we study Green measures of certain classes of Markov processes. In particular Brownian motion and processes with jump generators with different tails. The Green measures are represented as a sum of a singular and a regular…
The contact process is a particular case of birth-and-death processes on infinite particle configurations. We consider the contact models on locally compact separable metric spaces. We prove the existence of a one-parameter set of invariant…
We derive the Markov process equivalent to She-Leveque scaling in homogeneous and isotropic turbulence. The Markov process is a jump process for velocity increments $u(r)$ in scale $r$ in which the jumps occur randomly but with…
The gradient expansion is the fundamental organising principle underlying relativistic hydrodynamics, yet understanding its convergence properties for general nonlinear flows has posed a major challenge. We introduce a simple method to…
We study K-processes, which are Markov processes in a denumerable state space, all of whose elements are stable, with the exception of a single state, starting from which the process enters finite sets of stable states with uniform…
Using a perturbative approach, we investigate the parametric down-conversion process without the semi-classical approximation. A Wigner functional formalism, which incorporates both the spatiotemproal degrees of freedom and the…
Path-wise observables--functionals of stochastic trajectories--are at the heart of time-average statistical mechanics and are central to thermodynamic inequalities such as uncertainty relations, speed limits, and correlation-bounds. They…
We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a…