Related papers: Potential Theory of Truncated Stable Processes

Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…

In this paper we propose a wide class of truncated stochastic approximation procedures with moving random bounds. While we believe that the proposed class of procedures will find its way to a wider range of applications, the main motivation…

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

We consider a class of fully nonlinear integro-differential operators where the nonlocal integral has two components: the non-degenerate one corresponds to the $\alpha$-stable operator and the second one (possibly degenerate) corresponds to…

The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…

This article deals with the hypothesis test for the extremely heavy-tailed distributions with infinite mean or variance by using a truncated sample mean. We obtain three necessary and sufficient conditions under which the asymptotic…

We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the…

We consider a L\' evy process in $\R^d$ $ (d\geq 3)$ with the characteristic exponent \[ \Phi(\xi)=\frac{|\xi|^2}{\ln(1+|\xi|^2)}-1. \] The scale invariant Harnack inequality and apriori estimates of harmonic functions in H\" older spaces…

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

We analyze why the discretization of linear transport with asymmetric Hermite basis functions can be instable in quadratic norm. The main reason is that the finite truncation of the infinite moment linear system looses the skew-symmetry…

The paper is concerned with stochastic approximation procedures having three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function. We…

This paper deals with inference in a class of stable but nearly-unstable processes. Autoregressive processes are considered, in which the bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with…

The paper deals with the problem of estimating the M$^2$ (i.e. multivariate and multidimensional) spectral density function of a stationary random process or random field. We propose the $f$-truncated periodogram, i.e. a truncated…

We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f…

It was recently proven that the correlation function of the stationary version of a reflected L\'evy process is nonnegative, nonincreasing and convex. In another branch of the literature it was established that the mean value of the…

Let $X$ be a smooth projective variety of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$. Let $F_X:X\rightarrow X$ be the absolute Frobenius morphism, and $\E$ a torsion free sheaf on $X$. We give a upper bound…

We discuss an impact of various (path-wise) reflection-from-the barrier scenarios upon confining properties of a paradigmatic family of symmetric $\alpha $-stable L\'{e}vy processes, whose permanent residence in a finite interval on a line…

The perturbative expansion of static force and potential is reanalyzed concerning its practical applicability. A well behaved perturbative prediction is given by the integration of the renormalization group equation for the coupling…

Let $Z$ be a subordinate Brownian motion in ${\mathbb R}^d$, $d\ge 2$, via a subordinator with Laplace exponent $\phi$. We kill the process $Z$ upon exiting a bounded open set $D\subset {\mathbb R}^d$ to obtain the killed process $Z^D$, and…

We obtain two-sided bounds for the density of stochastic processes satisfying a weak H\"ormander condition. In particular we consider the cases when the support of the density is not the whole space and when the density has various…