Related papers: Nonlocal random motions: The trapping problem
We consider elliptic random walks in i.i.d. random environments on $\mathbb{Z}^d$. The main goal of this paper is to study under which ellipticity conditions local trapping occurs. Our main result is to exhibit an ellipticity criterion for…
We consider continuous time Markovian processes where populations of individual agents interact stochastically according to kinetic rules. Despite the increasing prominence of such models in fields ranging from biology to smart cities,…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…
Fractional Brownian motion can be represented as an integral of a deterministic kernel w.r.t. an ordinary Brownian motion either on infinite or compact interval. In previous literature fractional L\'evy processes are defined by integrating…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given…
Calibrating a L\'evy process usually requires characterizing its jump distribution. Traditionally this problem can be solved with nonparametric estimation using the empirical characteristic functions (ECF), assuming certain regularity, and…
Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical…
In this paper we extend models for the dynamic of the temperatures by considering random switching between Levy noises instead of Brownian motions, with a mean-reverting movement towards a seasonal periodic function. The use of Levy noises…
We consider a L\'evy process reflected at the origin with additional i.i.d. collapses that occur at Poisson epochs, where a collapse is a jump downward to a state which is a random fraction of the state just before the jump. We first study…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
We study stochastic equations of non-negative processes with jumps. The existence and uniqueness of strong solutions are established under Lipschitz and non-Lipschitz conditions. The comparison property of two solutions are proved under…
In this paper we address the problem of rare-event simulation for heavy-tailed L\'evy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for…
This article is concerned with stability analysis and stabilization of randomly switched nonlinear systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic…
We show that exact sampling of the first passage event can be done for a Levy process with unbounded variation, if the process can be embedded in a subordinated standard Brownian motion. By sampling a series of first exit events of the…
We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…
We establish via a probabilistic approach the quenched invariance principle for a class of long range random walks in independent (but not necessarily identically distributed) balanced random environments, with the transition probability…
We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which…
Donsker-type functional limit theorems are proved for empirical processes arising from discretely sampled increments of a univariate L\'evy process. In the asymptotic regime the sampling frequencies increase to infinity and the limiting…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…