Related papers: On the range of exponential functionals of L\'evy …
We study the L\'evy spin glass model, a fully connected model on $N$ vertices with heavy-tailed interactions governed by a power law distribution of order $0<\alpha<2.$ Our investigation is divided into three cases $0<\alpha<1$, $\alpha=1$,…
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable L\'evy process of index $ 1 < \alpha \le 2 $. The first kind is a function of the local time at the origin, and the…
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.…
Financial markets based on L\'evy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles.…
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…
In this article the relation between the tail behaviours of a free regular infinitely divisible (positively supported) probability measure and its L\'evy measure is studied. An important example of such a measure is the compound free…
The Lamperti correspondence gives a prominent role to two random time changes: the exponential functional of a L\'evy process drifting to $\infty$ and its inverse, the clock of the corresponding positive self-similar process. We describe…
Let $\Phi$ be a nuclear space and let $\Phi'_{\beta}$ denote its strong dual. In this work we establish the one-to-one correspondence between infinitely divisible measures on $\Phi'_{\beta}$ and L\'{e}vy processes taking values in…
In this paper, we establish the precise asymptotic behaviors of the tail probability and the transition density of a large class of isotropic L\'evy processes when the scaling order is between 0 and 2 including 2. We also obtain the precise…
In this paper we consider an interacting particle system in $\mathbb{R}^d$ modelled as a system of $N$ stochastic differential equations driven by L\'evy processes. The limiting behaviour as the size $N$ grows to infinity is achieved as a…
We consider discrete probability laws on the real line, whose characteristic functions are separated from zero. In particular, this class includes arbitrary discrete infinitely divisible laws and lattice probability laws, whose…
Path decomposition is performed to characterize the law of the pre/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy process taken up to an independent exponential time T: As a result, mainly the…
We study the ballistic L\'evy walk stemming from an infinite mean traveling time between collision events. Our study focuses on the density of spreading particles all starting from a common origin, which is limited by a `light' cone $-v_0…
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…
We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a…
By killing a stable L\'{e}vy process when it leaves the positive half-line, or by conditioning it to stay positive, or by conditioning it to hit 0 continuously, we obtain three different positive self-similar Markov processes which…
The existence-uniqueness theory for solutions to stochastic dynamic systems is always a significant theme and has received a huge attention. The objective of this article is to study the mentioned theory for stochastic functional…
In this paper, we study weak and strong transience of a class of Feller processes associated with pseudo-differential operators, the so-called L\'evy-type processes. As a main result, we derive Chung-Fuchs type conditions (in terms of the…
We suppose that a L\'evy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a…
We introduce a class of L\'{e}vy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions…