This article concerns the tail probabilities of a light-tailed Markov-modulated L\'evy process stopped at state-dependent Poisson rate. The tails are shown to decay exponentially rates given by unique positive and negative roots spectral abscissa certain matrix-valued function. We illustrate use our results with an application stationary distribution wealth in simple economic model which agents...

We investigate critical equilibrium and out of properties a ferromagnetic Ising model in one two dimension the presence long range interactions, $J_{ij}\propto r^{-(d+\sigma)}$. implement novel local dynamics on dynamical L\'evy lattice, that correctly reproduces static exponents known literature, as function interaction parameter $\sigma$. Due to its locality algorithm can be applied propertie...

In this article, we study the stochastic wave equation on entire space $\mathbb{R}^d$, driven by a space-time L\'evy white noise with possibly infinite variance (such as $\alpha$-stable noise). equation, is multiplied Lipschitz function $\sigma(u)$ of solution. We assume that spatial dimension $d=1$ or $d=2$. Under general conditions measure noise, prove existence solution, and show that, funct...

Results are obtained regarding the distribution of the ranked lengths of component intervals in the complement of the random set of times when a recurrent Markov process returns to its starting point. Various martingales are described in terms of the L evy measure of the Poisson point process of interval lengths on the local time scale. The martingales derived from the zero set of a one-dimensi...

The distributed computing analysis of the accuracy of automodel solutions for the Green's function of a wide class of superdiffusive transport of perturbation on a uniform background is carried out. The approximate automodel solutions have been suggested for the 1D transport equation with a model long-tailed step-length probability distribution function (PDF) with various power-law exponents. T...

[email protected] [email protected] Abstract: Consider the events fFn \ Sn 1 k=1 Fk = ;g, n 2 N, where (Fn) 1 n=1 is an i.i.d. sequence of stationary random subsets of a compact group G . A plausible conjecture is that these events will not occur in nitely often with positive probability if PfFi\Fj 6= ; jFjg > 0 a.s. for i 6= j. We present a counterexample to show that this conditio...

We study the effects of quantum corrections on transverse momentum broadening a fast parton passing through dense QCD matter. show that, at leading logarithmic accuracy distribution tends late times or equivalently for large system sizes $L$ to universal that only depends single scaling variable ${k}_{T}^{2}/{Q}_{s}^{2}$ where typical scale increases with time as $\mathrm{ln}\text{ }{Q}_{s}^{2}...

The Boltzmann-Gibbs statistical mechanics and the standard thermodynamics are very useful in the discussion of extensive systems. However, they are not good to study situations where nonextensive e ects occur, for instance, systems involving long-range interactions (e. g., d = 3 gravitation)[1, 2], long-range microscopic memory[3], and systems with a relevant (multi)fractal-like structure. On t...

In this paper we treat various aspects of a notion that is central in term rewriting namely that of descendants or residuals We address both rst order term rewriting and calculus their nitary as well as their in nitary variants A recurrent theme is the Parallel Moves Lemma Next to the classical notion of descendant we introduce an extended version known as origin tracking Origin tracking has ma...