Related papers: Persistence of integrated stable processes

Consider the first exit time $T_{a,b}$ from a finite interval $[-a,b]$ for an homogeneous fluctuating functional $X$ of a linear Brownian motion. We show the existence of a finite positive constant $\k$ such that…

Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…

We study the persistence probability for processes with stationary increments. Our results apply to a number of examples: sums of stationary correlated random variables whose scaling limit is fractional Brownian motion, random walks in…

We study a one-dimensional stochastic differential equation driven by a stable L\'evy process of order $\alpha$ with drift and diffusion coefficients $b,\sigma$. When $\alpha\in (1,2)$, we investigate pathwise uniqueness for this equation.…

Given a stable L\'{e}vy process $X=(X_t)_{0\le t\le T}$ of index $\alpha\in(1,2)$ with no negative jumps, and letting $S_t=\sup_{0\le s\le t}X_s$ denote its running supremum for $t\in [0,T]$, we consider the optimal prediction problem…

Let $X=\{X(t), t\geq 0\}$ be a Brownian motion or a spectrally negative stable process of index $1<\a<2$. Let $E=\{E(t),t\geq 0\}$ be the hitting time of a stable subordinator of index $0<\beta<1$ independent of $X$. We use a connection…

For the first time, we develop a convergent numerical method for the llinear integral equation derived by M.M. Lavrent'ev in 1964 with the goal to solve a coefficient inverse problem for a wave-like equation in 3D. The data are non…

This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski…

We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…

The first-exit time process of an inverse Gaussian L\'evy process is considered. The one-dimensional distribution functions of the process are obtained. They are not infinitely divisible and the tail probabilities decay exponentially. These…

We are interested in the differential equations satisfied by the density of the Geometric Stable processes $\mathcal{G}_{\alpha}^{\beta}=\left\{\mathcal{G}_{\alpha}^{\beta}(t);t\geq 0\right\} $, with stability \ index $% \alpha \in (0,2]$…

This paper studies the invertibility property of continuous time moving average processes driven by a L\'evy process. We provide of sufficient conditions for the recovery of the driving noise. Our assumptions are specified via the kernel…

Let $a\in (0,\infty)$. For a spectrally negative L\'evy process $X$ with infinite variation paths the resolvent of the process killed on hitting the two-point set $V=\{-a,a\}$ is identified. When further $X$ has no diffusion component the…

Recent fluctuation identities for $\alpha$-stable L\'evy processes have decomposed paths using generalised spherical polar coordinates revealing an underlying Markov Additive Process (MAP) for which a more advanced form of excursion theory…

We study spectral-theoretic properties of non-self-adjoint operators arising in the study of one-dimensional L\'evy processes with completely monotone jumps with a one-sided barrier. With no further assumptions, we provide an integral…

Based on the concept of a L\'evy copula to describe the dependence structure of a multivariate L\'evy process we present a new estimation procedure. We consider a parametric model for the marginal L\'evy processes as well as for the L\'evy…

Infinite horizon optimal stopping problems for a L\'evy processes with a two-sided reward function are considered. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. A…

In this paper, we prove a conditional H\"older stability estimate for the inverse spectral problem of the biharmonic operator. The proof employs the resolvent estimate and a Weyl-type law for the biharmonic operator which were obtained by…

We consider two-dimensional L\'evy processes reflected to stay in the positive quadrant. Our focus is on the non-standard regime when the mean of the free process is negative but the reflection vectors point away from the origin, so that…

We consider empirical processes generated by strictly stationary sequences of associated random variables. S. Louhichi established an invariance principle for such processes, assuming that the covariance function decays rapidly enough. We…