Related papers: The suprema of infinitely divisible processes

A novel approach is proposed to establish a sharp upper bound on the expected supremum of a separable martingale random field, serving as an alternative to classical universal chaining-based methods. The proposed approach begins by deriving…

In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by…

The solution to the infinite horizon optimal control problem for linear distributed time-delay systems is presented. The proposal is based on the use of the Cauchy solution for distributed time-delay systems. In contrast with previous…

In this paper, all of the restrictions that were previously required in order to obtain a hyperfinite unification for a set of physical theories have been removed. This yields the ultimate hyperfinite ultralogic unification for any set of…

We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…

For a stable process, we give an explicit formula for the potential measure of the process killed outside a bounded interval and the joint law of the overshoot, undershoot and undershoot from the maximum at exit from a bounded interval. We…

The article is devoted to the problem of applying the maximum principle for finding optimal control parameters in simulation tasks of interest for a variety of engineering and industrial systems and processes. Especially important is the…

We prove that under H\"ormander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an…

The Bessel point process is a rigid point process on the positive real line and its conditional measure on a bounded interval $[0,R]$ is almost surely an orthogonal polynomial ensemble. In this article, we show that if $R$ tends to…

Determining the relationship between quantum correlation sets is a long-standing open problem. The most well-studied part of the hierarchy is captured by the chain of inclusions $\mathcal C_q \subseteq \mathcal C_{qs} \subsetneq \mathcal…

Using an application of Schmidt's Subspace Theorem, this paper gives new transcendence criteria for rapidly converging infinite products of algebraic numbers. The paper also improves existing criteria for irrationality of products and…

We construct operator systems $\mathfrak C_I$ that are universal in the sense that all operator systems can be realized as their quotients. They satisfy the operator system lifting property. Without relying on the theorem by Kirchberg, we…

For $d\geq 1$ and $0<\beta<\alpha<2$, consider a family of pseudo differential operators $\{\Delta^{\alpha} + a^\beta \Delta^{\beta/2}; a \in [0, 1]\}$ that evolves continuously from $\Delta^{\alpha/2}$ to $ \Delta^{\alpha/2}+…

We give necessary and sufficient conditions for existence and infinite divisibility of $\alpha$-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.

In this article we derive formulas for the probability $P(\sup_{t\leq T} X(t)>u)$ $T>0$ and $P(\sup_{t<\infty} X(t)>u)$ where $X$ is a spectrally positive L\'evy process with infinite variation. The formulas are generalizations of the…

We show that the higher order linear differential equation possesses all solutions of infinite order under certain conditions by extending the work of authors about second order differential equation \cite{dsm2}.

We introduce the $\omega$-Vaught's conjecture, a strengthening of the infinitary Vaught's conjecture. We believe that if one were to prove the infinitary Vaught's conjecture in a structural way without using techniques from higher recursion…

We study translation invariant stochastic processes on $\mathbb{R}^d$ or $\mathbb{Z}^d$ whose diffraction spectrum or structure function $S(k)$, i.e. the Fourier transform of the truncated total pair correlation function, vanishes on an…

We consider the problem of finding a stopping time that minimises the $L^1$-distance to $\theta$, the time at which a L\'evy process attains its ultimate supremum. This problem was studied in [12] for a Brownian motion with drift and a…

In this paper we revisit the well-known technique of predicate abstraction to characterise performance attributes of system models incorporating probability. We recast the theory using expectation transformers, and identify transformer…