Related papers: Long-time behavior for a class of Feller processes

This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small…

A general connection between the characteristic function of a L\'evy process and loss of coherence of the statistical operator describing the center of mass degrees of freedom of a quantum system interacting through momentum transfer events…

We study a combination of the refracted and reflected L\'evy processes. Given a spectrally negative L\'evy process and two boundaries, it is reflected at the lower boundary while, whenever it is above the upper boundary, a linear drift at a…

We consider a continuous-space and continuous-time diffusion process under resetting with memory. A particle resets to a position chosen from its trajectory in the past according to a memory kernel. Depending on the form of the memory…

In the first part of the paper we prove various results on regularity of Feynman-Kac functionals of Hunt processes associated with time dependent semi-Dirichlet forms. In the second part we study the Cauchy problem for semilinear parabolic…

The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…

The purpose of this paper is to investigate the long time behaviour for a self-interacting diffusion and a self-interacting velocity jump process. While the diffusion case has already been studied for some particular potential function, the…

We analyze the extension of the well known relation between Brownian motion and Schroedinger equation to the family of Levy processes. We consider a Levy-Schroedinger equation where the usual kinetic energy operator - the Laplacian - is…

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'evy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'evy exponent $\psi(\la)$ is regularly varying at infinity with index $1<\beta\leq 2$ and satisfies some…

In this paper we consider a ring of $N\ge 1$ queues served by a single server in a cyclic order. After having served a queue (according to a service discipline that may vary from queue to queue), there is a switch-over period and then the…

For a L\'evy process $X$ on a finite time interval consider the probability that it exceeds some fixed threshold $x>0$ while staying below $x$ at the points of a regular grid. We establish exact asymptotic behavior of this probability as…

We study the long time behaviour of a large class of diffusion processes on $R^N$, generated by second order differential operators of (possibly) degenerate type. The operators that we consider {\em need not} satisfy the H\"ormander…

Let $\mathcal{K}\subset R^d$, $d\ge2$, be a smooth, bounded domain satisfying $0\in\mathcal{K}$, and let $f(t),\ t\ge0$, be a smooth, continuous, nondecreasing function satisfying $f(0)>1$. Define $D_t=f(t)\mathcal{K}\subset R^d$. Consider…

We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-dimensional L\'evy processes that drifts to plus infinity.…

L\'{e}vy walk is a popular and more `physical' model to describe the phenomena of superdiffusion, because of its finite velocity. The movements of particles are under the influences of external potentials almost at anytime and anywhere. In…

Time change is one of the most basic and very useful transformations for Markov processes. The time changed process can also be regarded as the trace of the original process on the support of the Revuz measure used in the time change. In…

In this manuscript, we continue with the systematic study of the speed of extinction of continuous state branching processes in L\'evy environments under more general branching mechanisms. Here, we deal with the weakly subcritical regime…

We construct in the small-time setting the upper and lower estimates for the transition probability density of a L\'evy process in $\rn$. Our approach relies on the complex analysis technique and the asymptotic analysis of the inverse…

Let $\tau(x)$ be the epoch of first entry into the interval $(x,\infty)$, $x>0$, of the reflected process $Y$ of a L\'evy process $X$, and define the overshoot $Z(x) = Y(\tau(x))-x$ and undershoot $z(x) = x - Y(\tau(x)-)$ of $Y$ at the…

We consider a class of L\'evy-type processes derived via a Doob-transform from L\'evy processes conditioned by a control function called potential. These processes have position-dependent and generally unbounded components, with stationary…