Related papers: Unimodality of hitting times for stable processes

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…

In this paper, we simulate sample paths of a class of symmetric $\alpha$-stable processes using their series expression. We will develop a result in the approximation of shot-noise series. And finally, we will get a convergence rate for the…

Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…

For a time-changed symmetric $\alpha$-stable process killed upon hitting zero, under the condition of entrance from infinity, we prove the existence and uniqueness of quasi-stationary distribution (QSD). The exponential convergence to the…

In this paper, we establish the existence of moments and moment estimates for L\'evy-type processes. We discuss whether the existence of moments is a time dependent distributional property, give sufficient conditions for the existence of…

We present a novel theoretical result on estimation of local time and occupation time measure of an {\alpha}-stable L\'evy process with {\alpha} in (1, 2). Our approach is based upon computing the conditional expectation of the desired…

Motivated by the recent results of Nualart and Xu \cite{Nualart} concerning limits laws for occupation times of one dimensional symmetric stable processes, this paper proves a decomposition for functionals of one dimensional symmetric…

We prove sharp two-sided estimates on the tail probability of the first hitting time of bounded interval as well as its asymptotic behaviour for general non-symmetric processes which satisfy an integral condition \[ \int_0^{\infty}…

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…

In this paper we present the asymptotic analysis of the realised quadratic variation for multivariate symmetric $\beta$-stable L\'evy processes, $\beta \in (0,2)$, and certain pure jump semimartingales. The main focus is on derivation of…

Stable distributions are a celebrated class of probability laws used in various fields. The $\alpha$-stable process, and its exponentially tempered counterpart, the Classical Tempered Stable (CTS) process, are also prominent examples of…

Small-space and large-time estimates and asymptotic expansion of the distribution function and (the derivatives of) the density function of hitting times of points for symmetric L\'evy processes are studied. The L\'evy measure is assumed to…

Multistable processes, that is, processes which are, at each "time", tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is…

Let $X=\{X_{t},t\in R_{+}\}$ be a symmetric L\'{e}vy process with local time $\{L^{x}_{t} ; (x,t)\in R^{1}\times R^{1}_{+}\}$. When the L\'{e}vy exponent $\psi(\la)$ is regularly varying at zero with index $1<\beta\leq 2$, and satisfies…

Let ${\mathcal A}$ be the ${\mathcal L}^q-$functional of a stable L\'evy process starting from one and killed when crossing zero. We observe that ${\mathcal A}$ can be represented as the independent quotient of two infinite products of…

First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…

For the supercritical contact process on the hyper-cubic lattice started from a single infection at the origin and conditioned on survival, we establish two uniformity results for the hitting times $t(x)$, defined for each site $x$ as the…

We prove that classical and free Brownian motions with initial distributions are unimodal for sufficiently large time, under some assumption on the initial distributions. The assumption is almost optimal in some sense. Similar results are…

Additive processes are obtained from L\'{e}vy ones by relaxing the condition of stationary increments, hence they are spatially (but not temporally) homogeneous. By analogy with the case of time-homogeneous Markov processes, one can define…

We prove that for any $\alpha$-mixing stationnary process the hitting time of any $n$-string $A_n$ converges, when suitably normalized, to an exponential law. We identify the normalization constant $\lambda(A_n)$. A similar statement holds…