Related papers: Jump processes as Generalized Gradient Flows
In this paper we introduce non-decreasing jump processes with independent and time non-homogeneous increments. Although they are not L\'evy processes, they somehow generalize subordinators in the sense that their Laplace exponents are…
We present an It\^o formula for the $L_p$-norm of jump processes having stochastic differentials in $L_p$-spaces. The main results extend well-known theorems of Krylov to the case of processes with jumps, and which can be used to prove…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
We consider a class of discrete $q$-state spin models defined in terms of a translation-invariant quasilocal specification with discrete clock-rotation invariance which have extremal Gibbs measures $\mu'_{\varphi}$ labeled by the…
In this paper, we discuss general criteria of limsup law of iterated logarithm (LIL) for continuous-time Markov processes. We consider minimal assumptions for LILs to hold at zero(at infinity, respectively) in general metric measure spaces.…
We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite…
In a previous work we devised a framework to derive generalised gradient systems for an evolution equation from the large deviations of an underlying microscopic system, in the spirit of the Onsager-Machlup relations. Of particular interest…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…
Markov-modulated fluid queues (MMFQs) are a powerful modeling framework for analyzing the performance of computer and communication systems. Their distinguishing feature is that the underlying Markov process evolves on a continuous state…
In the presence of quantum measurements with direct photon detection the evolution of open quantum systems is usually described by stochastic master equations with jumps. Heuristically, from these equations one can obtain diffusion models…
Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…
We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple…
Tau leap schemes were originally designed for the efficient time stepping of discrete state and continuous in time Markov processes arising in stochastic chemical kinetics. Previous convergence results on tau leaping schemes have been…
Continuing from arXiv:2102.01917v2, in this paper, we discuss general criteria and forms of liminf laws of iterated logarithm (LIL) for continuous-time Markov processes. Under some minimal assumptions, which are weaker than those in…
In this paper, we proved moderate deviation principles for a fully coupled two-time-scale stochastic systems, where the slow process is given by stochastic differential equations with small noise, while the fast process is a rapidly…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
We employ the quantum jump trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive…
We study a model of an infinite system of point particles in $\mathds{R}^d$ performing random jumps with attraction. The system's states are probability measures on the space of particle configurations, and their evolution is described by…
Markovian open quantum systems are governed by the Lindblad master equation where the dissipation contains two parts, i.e., the anti-Hermitian operator and the quantum jumps, which share a common dissipation rate. We generalize the Lindblad…
Our study addresses the inference of jumps (i.e. sets of discontinuities) within multivariate signals from noisy observations in the non-parametric regression setting. Departing from standard analytical approaches, we propose a new…