Related papers: A decomposition for additive functional of Levy pr…
Suppose that Y(t) is a d-dimensional Levy symmetric process for which its Levy measure differs from the Levy measure of the isotropic alpha-stable process (0<alpha<2) by a finite signed measure. For a bounded Lipschitz set D we compare the…
As an analogue to the explicit formula in the stable case, the asymptotic behavior at the origin of the renormalized zero resolvent of one-dimensional L\'evy processes is studied under certain regular variation conditions on the…
For a L\'evy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval $(r,\infty)$, the sojourn time in the interval $(-\infty,r]$, and the last exit time…
It is proved that the two-sided exits of a Levy process are proper, i.e. not a.s. equal to their one-sided counterparts, if and only if said process is not a subordinator or the negative of a subordinator. Furthermore, Levy processes are…
The goal of this paper is to derive a formula for the finite dimensional joint characteristic function (the Fourier transform of the finite dimensional distribution) of the coupled process ${(W_{t},L_{t}^{A}):t\in \lbrack 0,\infty)}$, where…
The L2-approximation of occupation and local times of a symmetric $\alpha$-stable L{\'e}vy process from high frequency discrete time observations is studied. The standard Riemann sum estimators are shown to be asymptotically efficient when…
In this paper we study a one-dimensional space-discrete transport equation subject to additive Levy forcing. The explicit form of the solutions allows their analytic study. In particular we discuss the invariance of the covariance structure…
This paper aims at semi-parametrically estimating the input process to a L\'evy-driven queue by sampling the workload process at Poisson times. We construct a method-of-moments based estimator for the L\'evy process' characteristic…
We continue the investigation of the Levy processes on a q-deformed full Fock space started in a previous paper. First, we show that the vacuum vector is cyclic and separating for the algebra generated by such a process. Next, we describe a…
In this article, we introduce Mittag-Leffler L\'evy process and provide two alternative representations of this process. First, in terms of Laplace transform of the marginal densities and next as a subordinated stochastic process. Both…
The classical notion of L\'evy process is generalized to one that takes as its values probabilities on a first order model equipped with a commutative semigroup. This is achieved by applying a convolution product on definable probabilities…
Using the Lyapunov criteria arguments, we find sufficient conditions on explosion/nonexplosion for continuous-state branching processes with competition in L\'evy random environment. In particular, we identify the necessary and sufficient…
We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely…
For a general free L\'evy process, we prove the existence of its higher variation processes as limits in distribution, and identify the limits in terms of the L\'evy-It\^o representation of the original process. For a general free compound…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties,…
In this work, we investigate the fine regularity of L\'evy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities…
We prove functional, distributional limit theorems for the occupation times of pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting processes are tied down Mittag-Leffler processes and the…
Let $X=\{X(t),t\in R_+\}$ be a real-valued symmetric L\'{e}vy process with continuous local times $\{L^x_t,(t,x)\in R_+\times R\}$ and characteristic function $Ee^{i\lambda X(t)}=e^{-t\psi(\lambda)}$. Let…
For spectrally negative L\'evy processes, adapting an approach from \cite{BoLi:sub1} we identify joint Laplace transforms involving local times evaluated at either the first passage times, or independent exponential times, or inverse local…