Related papers: Occupation Times for Jump Processes

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…

A comparison theorem for state-dependent regime-switching diffusion processes is established, which enables us to control pathwisely the evolution of the state-dependent switching component simply by Markov chains. Moreover, a sharp…

We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…

The paper deals with the asymptotic properties of a random jump process in a high contrast periodic medium in $\mathbb R^d$, $d\geq 1$. We show that if the coordinates of the random jump process in $\mathbb R^d$ are equipped with an extra…

The discrete class algorithm presented in this paper is an efficient simulation tool for stochastic processes governed by a reasonably small set of transition rates. The algorithm is presented, its performance compared to prevailing methods…

We prove sharp two-sided bounds of the fundamental solution for an integro-differential operator of order $\alpha \in (0,2)$ that generates a $d$-dimensional Markov process. The corresponding Dirichlet form is comparable to that of $d$…

Semi-Markov processes are Markovian processes in which the firing time of the transitions is modelled by probabilistic distributions over positive reals interpreted as the probability of firing a transition at a certain moment in time. In…

In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack inequality and H\"older regularity hold for parabolic…

We consider a discrete-time $d$-dimensional process $\{\boldsymbol{X}_n\}=\{(X_{1,n},X_{2,n},...,X_{d,n})\}$ on $\mathbb{Z}^d$ with a background process $\{J_n\}$ on a countable set $S_0$, where individual processes…

We survey the recent development of the DeGiorgi-Nash-Moser-Aronson type theory for a class of symmetric jump processes(or equivalently, a class of symmetric integro-differential operators). We focus on the sharp two-sided estimates for the…

In the last two decades the study of random instances of constraint satisfaction problems (CSPs) has flourished across several disciplines, including computer science, mathematics and physics. The diversity of the developed methods, on the…

We consider a class of continuous time Markov chains on $\Z^d$. These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, we show that harmonic functions associated with these Markov chains are…

Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…

Markov jump processes are continuous-time stochastic processes which describe dynamical systems evolving in discrete state spaces. These processes find wide application in the natural sciences and machine learning, but their inference is…

It has been shown by Bertoin and Yor (2002) that the law of positive self-similar Markov processes (pssMps) that only jump downwards and do not hit zero in finite time are uniquely determined by their entire moments for which explicit…

We prove a robust super-hedging duality result for path-dependent options on assets with jumps, in a continuous time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some…

By making full use of heat kernel estimates, we establish the integral tests on the zero-one laws of upper and lower bounds for the sample path ranges of symmetric Markov processes. In particular, these results concerning on upper rate…

A $p$-jump process is a piecewise deterministic Markov process with jumps by a factor of $p$. We prove a limit theorem for such processes on the unit interval. Via duality with respect to probability generating functions, we deduce limiting…

We establish a functional limit theorem for the joint-law of occupations near and away from indifferent fixed points of interval maps, and of waits for the occupations away from these points, in the sense of strong distributional…

We study distributions of meeting times for finite symmetric Markov chains. For Markov kernels defined on large state spaces which satisfy certain weak inhomogeneity in return probabilities of points up to large numbers of steps, we obtain…