Related papers: Spectral representations of quasi-infinitely divis…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
Determinantal and permanental processes are point processes with a correlation function given by a determinant or a permanent. Their atoms exhibit mutual attraction of repulsion, thus these processes are very far from the uncorrelated…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
We define a large class of continuous time multifractal random measures and processes with arbitrary log-infinitely divisible exact or asymptotic scaling law. These processes generalize within a unified framework both the recently defined…
Cylindrical probability measures are finitely additive measures on Banach spaces that have sigma-additive projections to Euclidean spaces of all dimensions. They are naturally associated to notions of weak (cylindrical) random variable and…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…
We consider a new class $\boldsymbol{Q}$ of distribution functions $F$ that have the property of rational-infinite divisibility: there exist some infinitely divisible distribution functions $F_1$ and $F_2$ such that $F_1=F*F_2$. A…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
We develop a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: the first, which we largely focus on, features a…
Across many plasma applications, the underlying phenomena and interactions among the involved processes are known to exhibit three-dimensional characteristics. Furthermore, the global properties and evolution of plasma systems are often…
This is a short review on the thermal, spectral representation in the real-time version of the finite temperature quantum field theory. After presenting a clear derivation of the spectral representation, we discuss the properties of its…
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon, which allows to describe simultaneously, unpolarized and polarized Deep Inelastic Scattering data. Some predictions from a…
In this paper, we discuss the representability almost everywhere (a.e.) in the plane of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite…
We introduce a class of multi-scale systems with discrete time, motivated by the problem of inviscid limit in fluid dynamics in the presence of small-scale noise. These systems are infinite-dimensional and defined on a scale-invariant…
Let $X^{(\mu)}(ds)$ be an $\mathbb{R}^d$-valued homogeneous independently scattered random measure over $\mathbb{R}$ having $\mu$ as the distribution of $X^{(\mu)}((t,t+1])$. Let $f(s)$ be a nonrandom measurable function on an open interval…
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
We discuss the (re-)construction of quasiprobability representations from generic measurements, including noisy ones. Based on the measurement under study, quasiprobabilities and the associated concept of nonclassicality are introduced. A…