Related papers: Closed-form solutions for the L\'evy-stable distri…
We explore the spectral properties of the $4$-fermion Sachdev-Ye-Kitaev model with interaction sourced from a L\'evy Stable (fat-tailed) distribution. L\'evy random matrices are known to demonstrate non-ergodic behaviour through the…
We study the electromagnetic transmission $T$ through one-dimensional (1D) photonic heterostructures whose random layer thicknesses follow a long-tailed distribution --L\'evy-type distribution. Based on recent predictions made for 1D…
The ordinary Levy motion is a random process whose stationary independent increments are statistically self-affine and distributed with a stable probability law characterized by the Levy index alpha, 0 < alpha < 2. The divergence of…
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their…
We prove a universal approximation theorem that allows to approximate continuous functionals of c\`adl\`ag (rough) paths uniformly in time and on compact sets of paths via linear functionals of their time-extended signature. Our main…
We show that a gas thermometer in contact with a stationary classical system out of thermal (Boltzmann) equilibrium evolves, under very general conditions, towards a state characterized by a Levy velocity distribution. Our approach is based…
Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…
A novel model of transport is proposed to explain power law current transients and memory phenomena observed in partially ordered arrays of semiconducting nanocrystals. The model describes electron transport by a stationary Levy process of…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean-Vlasov, driven by a…
In [16], under mild conditions, a Wiener-Hopf type factorization is derived for the exponential functional of proper L\'evy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by…
The McLennan-Zubarev steady state distribution is studied in the connection with fluctuation theorems. We derive the McLennan-Zubarev steady state distribution from the nonequilibrium detailed balance relation. Then, considering the…
We introduce a notion of geometric tempering using exponentially-dampened Mittag-Leffler tempering functions and closely investigate the univariate case. Characteristic exponents and cumulants are calculated, as well as spectral densities.…
We show that a conditional characteristic function of generalized L\'evy stochastic areas can be viewed as a product a selfdecomposable distribution (i.e., L\'evy class L distribution) and its background driving characteristic function.…
We exploit the asymptotic normality of the extreme value theory (EVT) based estimators of the parameters of a symmetric L\'evy-stable distribution, to construct confidence intervals. The accuracy of these intervals is evaluated through a…
We present an extensive analysis of transport properties in superdiffusive two dimensional quenched random media, obtained by packing disks with radii distributed according to a L\'evy law. We consider transport and scaling properties in…
The family of stable distributions received extensive applications in many fields of studies since it incorporates both the skewness and heavy tails. In this paper, we introduce a package written in the R language called alphastable. The…
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…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…