Related papers: Operator-stable-like Processes
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
Branching-stable processes have recently appeared as counterparts of stable subordinators, when addition of real variables is replaced by branching mechanism for point processes. Here, we are interested in their domains of attraction and…
This paper addresses the estimation of locally stationary long-range dependent processes, a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency. A time-varying…
The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related with the stability results for the Kirk-multistep and Kirk-SP…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
In many contexts such as queuing theory, spatial statistics, geostatistics and meteorology, data are observed at irregular spatial positions. One model of this situation involves considering the observation points as generated by a Poisson…
Environmental data science for spatial extremes has traditionally relied heavily on max-stable processes. Even though the popularity of these models has perhaps peaked with statisticians, they are still perceived and considered as the…
We consider a class of fully nonlinear integro-differential operators where the nonlocal integral has two components: the non-degenerate one corresponds to the $\alpha$-stable operator and the second one (possibly degenerate) corresponds to…
In this paper we introduce and study some Hilbert-type operators acting from the function spaces into the sequence spaces. We give some sufficient and necessary conditions for the boundedness and compactness of these Hilbert-type operators.…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered…
While max-stable processes are typically written as pointwise maxima over an infinite number of stochastic processes, in this paper, we consider a family of representations based on $\ell^p$ norms. This family includes both the construction…
A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…
In this paper we estimate both the Hurst and the stable indices of a H-self-similar stable process. More precisely, let $X$ be a $H$-sssi (self-similar stationary increments) symmetric $\alpha$-stable process. The process $X$ is observed at…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
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…
We derive normal approximation results for a class of stabilizing functionals of binomial or Poisson point process, that are not necessarily expressible as sums of certain score functions. Our approach is based on a flexible notion of the…
Emerging network scenarios require the development of solid large-scale situated systems. Unfortunately, the diffusion/aggregation computational processes therein often introduce a source of complexity that hampers predictability of the…