Related papers: Sinai's condition for real valued L\'{e}vy process…
In this paper, we derive identities for the upward and downward exit problems and resolvents for a process whose motion changes between two L\'evy processes if it is above (or below) a barrier $b$ and coincides with a Poissonian arrival…
Sinai's random walk in random environment shows interesting patterns on the exponential time scale. We characterize the patterns that appear on infinitely many time scales after appropriate rescaling (a functional law of iterated…
In this paper, we study the L\'evy process time-changed by independent L\'evy subordinators, namely, the incomplete gamma subordinator, the $\epsilon$-jumps incomplete gamma subordinator and tempered incomplete gamma subordinator. We derive…
We study the stationary properties as well as the non-stationary dynamics of the one-dimensional partially asymmetric exclusion process with position dependent random hop rates. In a finite system of $L$ sites the stationary current, $J$,…
For a spectrally negative L\'evy process (snLp) $X$, killed according to a rate that is a function $\omega$ of its position, we analyse the exit probability of the one-sided upwards-passage problem. When $\omega$ is strictly positive, this…
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…
A necessary and sufficient condition for a L\'evy process $X$ to stay positive, in probability, near 0, which arises in studies of Chung-type laws for $X$ near 0, is given in terms of the characteristics of $X$.
Sinai's walk is a recurrent one-dimensional nearest-neighbor random walk in random environment. It is known for a phenomenon of strong localization, namely, the walk spends almost all time at or near the bottom of deep valleys of the…
In this paper we study a spectrally negative L\'{e}vy process that is reflected at its draw-down level whenever a draw-down time from the running supremum arrives. Using an excursion-theoretical approach, for such a reflected process we…
The Levy Walk is the process with continuous sample paths which arises from consecutive linear motions of i.i.d. lengths with i.i.d. directions. Assuming speed 1 and motions in the domain of beta-stable attraction, we prove functional limit…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
Let X be a critical branching L{\'e}vy process whose offspring distribution is in the domain of attraction of a stable random variable. We study the tail probability of the maximum location ever reached by a particle in two different…
The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measure of the height of an excursion above the minimum. We…
We study the speed of extinction of continuous state branching processes in a L\'evy environment, where the associated L\'evy process oscillates. Assuming that the L\'evy process satisfies the Spitzer's condition and the existence of some…
The running infimum of a Levy process relative to its point of issue is know to have the same range that of the negative of a certain subordinator. Conditioning a Levy process issued from a strictly positive value to stay positive may…
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…
In this paper we study a queue with L\'evy input, without imposing any a priori assumption on the jumps being one-sided. The focus is on computing the transforms of all sorts of quantities related to the transient workload, assuming the…
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…
In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed L\'{e}vy process $X$ in $\mathbb{R}$. Let $\zeta$ denote the extinction time, $M_t$ be the maximal…
We consider a Lindley process with Laplace distributed space increments. We obtain closed form recursive expressions for the density function of the position of the process and for its first exit time distribution from the domain $[0,h]$.…