Related papers: Right inverses of L\'{e}vy processes

We consider finite and infinite systems of particles on the real line and half-line evolving in continuous time. Hereby, the particles are driven by i.i.d. L\'{e}vy processes endowed with rank-dependent drift and diffusion coefficients. In…

For a spectrally negative L\'evy process $X$, we study the following distribution: $$ \mathbb{E}_x \left[ \mathrm{e}^{- q \int_0^t \mathbf{1}_{(a,b)} (X_s) \mathrm{d}s } ; X_t \in \mathrm{d}y \right], $$ where $-\infty \leq a < b < \infty$,…

We prove that the norm of a $d$-dimensional L\'evy process possesses a finite second moment if and only if the convex distance between an appropriately rescaled process at time $t$ and a standard Gaussian vector is integrable in time with…

We consider the passage time problem for L\'evy processes, emphasising heavy tailed cases. Results are obtained under quite mild assumptions, namely, drift to $-\infty$ a.s. of the process, possibly at a linear rate (the finite mean case),…

Let {X_{t_1,t_2}: t_1,t_2 >= 0} be a two-parameter L\'evy process on R^d. We study basic properties of the one-parameter process {X_{x(t),y(t)}: t \in T} where x and y are, respectively, nondecreasing and nonincreasing nonnegative…

This study considers a continuous-review inventory model for a single item with two replenishment modes. Replenishments may occur continuously at any time with a higher unit cost, or at discrete times governed by Poisson arrivals with a…

We consider a continuous time version of Cramer's theorem with nonnegative summands $ S_t=\frac{1}{t}\sum_{i:\tau_i\le t}\xi_i, t \to\infty, $ where $(\tau_i,\xi_i)_{i\ge 1}$ is a sequence of random variables such that $tS_t$ is a random…

We consider spin systems on $\Z$ (i.e.\ interacting particle systems on $\Z$ in which each coordinate only has two possible values and only one coordinate changes in each transition) whose rates are determined by another process, called a…

We suppose that a L\'evy process is observed at discrete time points. A rather general construction of minimum-distance estimators is shown to give consistent estimators of the L\'evy-Khinchine characteristics as the number of observations…

We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…

We consider a branching stable process with positive jumps, i.e. a continuous-time branching process in which the particles evolve independently as stable L{\'e}vy processes with positive jumps. Assuming the branching mechanism is critical…

We investigate the behavior of L\'{e}vy processes with convolution equivalent L\'{e}vy measures, up to the time of first passage over a high level u. Such problems arise naturally in the context of insurance risk where u is the initial…

An $\al$-permanental process $\{X_{ t},t\in T \}$ is a stochastic process determined by a kernel $K=\{K(s,t),s,t\in T \}$, with the property that for all $t_{1},\ldots,t_{n}\in T $, $ |I+K( t_{1},\ldots,t_{n}) S|^{- \al} $ is the Laplace…

This paper studies a class of optimal multiple stopping problems driven by L\'evy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real…

In this article, the problem of semi-parametric inference on the parameters of a multidimensional L\'{e}vy process $L_t$ with independent components based on the low-frequency observations of the corresponding time-changed L\'{e}vy process…

Semi-Levy process is an additive process with periodically stationary increments. In particular, it is a generalization of Levy process. The dichotomy of recurrence and transience of Levy processes is well known, but this is not necessarily…

We study whether a multivariate L\'evy-driven moving average process can shadow arbitrarily closely any continuous path, starting from the present value of the process, with positive conditional probability, which we call the conditional…

By using absolutely continuous lower bounds of the L\'evy measure, explicit gradient estimates are derived for the semigroup of the corresponding L\'evy process with a linear drift. A derivative formula is presented for the conditional…

In this paper our first goal is to give precise definition of the L\'evy bridges with random length. Our second task is to establish the Markov property of this process with respect to its completed natural filtration and thus with respect…

Iksanov and Pilipenko (2023) defined a skew stable L\'{e}vy process as a scaling limit of a sequence of perturbed at $0$ symmetric stable L\'{e}vy processes (continuous-time processes). Here, we provide a simpler construction of the skew…