相关论文: On the reducibility of affine models with dependen…
In this paper, we consider function-indexed normalized weighted integrated periodograms for equidistantly sampled multivariate continuous-time state space models which are multivariate continuous-time ARMA processes. Thereby, the sampling…
Process convolutions yield random fields with flexible marginal distributions and dependence beyond Gaussianity, but statistical inference is often hampered by a lack of closed-form marginal distributions, and simulation-based inference may…
The density linear response function for an inhomogeneous system of electrons in equilibrium with an array of fixed ions is considered. Two routes to its evaluation for extreme conditions (e.g., warm dense matter) are considered. The first…
We prove various low-energy decomposition results, showing that we can decompose a finite set $A\subset \mathbb{F}_p$ satisfying $|A|<p^{5/8}$, into $A = S\sqcup T$ so that, for a non-degenerate quadratic $f\in \mathbb{F}_p[x,y]$, we have…
This article carries out a qualitative analysis on a system of integral equations of the Hardy--Sobolev type. Namely, results concerning Liouville type properties and the fast and slow decay rates of positive solutions for the system are…
In this work, we investigate the fine regularity of L\'evy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities…
A decade ago Rhie \et (Phys. Rev. Lett. {\bf 90}, 247201 (2003)) reported that when ferromagnetic nickel is subject to an intense ultrashort laser pulse, its exchange splitting is reduced quickly. But to simulate such reduction remains a…
In this article, we introduce an infinite-dimensional analogue of the $\alpha$-stable L\'evy motion, defined as a L\'evy process $Z=\{Z(t)\}_{t \geq 0}$ with values in the space $\mathbb{D}$ of c\`adl\`ag functions on $[0,1]$, equipped with…
Score-based diffusion models have demonstrated outstanding empirical performance in machine learning and artificial intelligence, particularly in generating high-quality new samples from complex probability distributions. Improving the…
We study the asymptotic behaviour of least squares estimators in regression models for long-range dependent random fields observed on spheres. The least squares estimator can be given as a weighted functional of long-range dependent random…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
In this article, we first review the connection between L\'evy processes and infinitely divisible random variables, and the classification of infinitely divisible distributions. Using this connection and the L\'evy-Khinchine representation…
We study small time bounds for transition densities of convolution semigroups corresponding to pure jump L\'evy processes in $\mathbb{R}^{d}$, $d \geq 1$, including those with jumping kernels exponentially and subexponentially localized at…
In this note we present a new short and direct proof of L\'{e}vy's continuity theorem in arbitrary dimension $d$, which does not rely on Prohorov's theorem, Helly's selection theorem or the uniqueness theorem for characteristic functions.…
{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a…
In this paper, we study nonparametric estimation of the L\'{e}vy density for L\'{e}vy processes, with and without Brownian component. For this, we consider $n$ discrete time observations with step $\Delta$. The asymptotic framework is: $n$…
Given a L\'evy process $L$, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time $T$ based on i.i.d. sample from $L_{T}.$ Our approach is based on the genuine use of…
For L\'evy processes with exponentially decaying tails of the L\'evy density, we derive integral representations for the joint cpdf $V$ of $(X_T, \bar X_T,\tau_T)$ (the process, its supremum evaluated at $T<+\infty$, and the first time at…
We derive explicit valuation formulae for an exotic path-dependent interest rate derivative, namely an option on the composition of LIBOR rates. The formulae are based on Fourier transform methods for option pricing. We consider two models…
In this paper we study the domain of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of L\'evy- and L\'evy-type…