Related papers: A factorization of a L\'evy process over a phase-t…
Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+{\alpha}}$, with $0 < {\alpha} < 2$. The Levy parameter ${\alpha}$ was measured from $P(x)$,…
Let $X$ be an elliptic curve or a ramifying hyperelliptic curve over $\mathbb F_q$. We will discuss how to factorize the coefficients of the exponential and logarithm series for a Hayes module over such a curve. This allows us to obtain…
In this paper, we consider a type of time-changed Markov process, where the time-change is an inverse killed subordinator. This can be seen as an extension of Chen (Chen, Z., Time fractional equations and probabilistic representation, Chaos…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
Several long-time limit theorems of one-dimensional L\'{e}vy processes weighted and normalized by functions of the local time are studied. The long-time limits are taken via certain families of random times, called clocks: exponential…
In this paper the Wiener--Hopf factorisation problem is presented in a unified framework with the Riemann--Hilbert factorisation. This allows to establish the exact relationship between the two types of factorisation. In particular, in the…
We introduce and consider a certain probability question involving elementary number theory and the likelihood that a fixed prime will appear in a certain recursively defined factorization of an integer. We derive several convergent…
We study the spectral form factor (SFF) of general topological gravity in the limit of large time and fixed temperature. It has been observed recently that in this limit, called the tau-scaling limit, the genus expansion of the SFF can be…
The first passage time process of a L\'evy subordinator with heavy-tailed L\'evy measure has long-range dependent paths. The random fluctuations that appear under two natural schemes of summation and time scaling of such stochastic…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
This paper introduces a new method for constructing approximate solutions to a class of Wiener--Hopf equations. This is particularly useful since exact solutions of this class of Wiener--Hopf equations, at the moment, cannot be obtained.…
We revisit the proof of the perturbative QCD factorization for the exclusive processes $\rho \gamma^{\star} \to \pi(\rho)$ at the two-parton twist-3 level. It is pointed out that the residual collinear divergences observed in the…
We present the path-sum formulation for $\mathsf{OE}[\mathsf{H}](t',t)=\mathcal{T}\,\text{exp}\big(\int_{t}^{t'}\!\mathsf{H}(\tau)\,d\tau\big)$, the time-ordered exponential of a time-dependent matrix $\mathsf{H}(t)$. The path-sum…
We consider matrix functions with certain invariance under inversion in the unit circle. If such a function satisfies a positivity assumption on the unit circle, then only zero partial indices appear in its Riemann-Hilbert (Wiener-Hopf)…
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…
We derive a moment formula for generalized fractional polynomial processes, i.e., for polynomial-preserving Markov processes time-changed by an inverse L\'evy-subordinator. If the time change is inverse $\alpha$-stable, the time-derivative…
In this article, we consider the reconstruction of $\rho(t)$ in the (time-fractional) diffusion equation $(\partial_t^\alpha-\triangle)u(x,t)=\rho(t)g(x)$ ($0<\alpha \le 1$) by the observation at a single point $x_0$. We are mainly…
A leading-twist factorization formula is derived for the longitudinal structure function in the x -->1 limit of deeply inelastic scattering. This is achieved by defining a new jet function which is gauge independent and probes the…
We provide asymptotic results and develop high frequency statistical procedures for time-changed L\'evy processes sampled at random instants. The sampling times are given by first hitting times of symmetric barriers whose distance with…
Kuznetsov et al. (2011) and Kuznetsov and Pardo (2013) introduced the family of Hypergeometric L\'evy processes. They appear naturally in the study of fluctuations of stable processes when one analyses stable processes through the theory of…