We establish the large deviation principle for slow variables in slow-fast dynamical system driven by both Brownian noises and L\'evy noises. The fast evolve at much faster time scale than variables, but they are fully inter-dependent. study asymptotics of logarithmic functionals three regimes based on viscosity solutions to Cauchy problem a sequence partial integro-differential equations. also...

L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in micro macro dynamics. From perspective random theory, here we investigate dynamics walks under influences constant force field combined with harmonic potential. Utilizing Hermite polynomial approximation deal spatiotemporally couple...

For a spectrally negative L\'evy process, scale functions appear in the solution of two-sided exit problems, and particular relation with Laplace transform first time it exits closed interval. In this paper, we consider more general functionals, which can depend simultaneously on values process its supremum up to time. These quantities will be expressed terms generalized functions, defined usin...

We design a normalizing strategy for orthogonal term rewriting systems (OTRSs), which is a generalization of the call-by-need strategy of Huet-L evy 4]. The redexes contracted in our strategy are essential in the sense that they have \descendants" under any reduction of a given term. There is an essential redex in any term not in normal form. We further show that contraction of the innermost es...

1 2 It’s Time for Some “Site”-Seeing: Novel Tools to Monitor the Ubiquitin Landscape in 3 Arabidopsis thaliana 4 5 Alan Walton,a,b,c,d,1 Elisabeth Stes,a,b,c,d,1 Nicolas Cybulski,a,b Michiel Van Bel,a,b Sabrina 6 Iñigo,a,b Astrid Nagels Durand,a,b Evy Timmerman,c,d Jefri Heyman,a,b Laurens Pauwels,a,b 7 Lieven De Veylder,a,b Alain Goossens,a,b Ive De Smet,a,b Frederik Coppens,a,b Sofie 8 Goorma...

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...

We prove simple general formulas for expectations of functions a L\'evy process and its running extremum. Under additional conditions, we derive analytical using the Fourier/Laplace inversion Wiener-Hopf factorization, discuss efficient numerical methods realization these formulas. As applications, cumulative probability distribution function maximum price option to exchange power stock are cal...

We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by Chen et al. [Nature Mater., 14, 589 (2015)]. derive the nonhomogeneous space time, hyperbolic partial differential equation for probability density function ...

We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations a L\'evy process. The first procedure relies on reordering independently sampled normal increments thus avoids tuning parameters. functionality this method is consequence small time predominance component, presence exchangeable structures, fast convergence em...