相关论文: Spectra of Poisson functionals and applications in…

Suppose we observe a trajectory of length $n$ from an exponentially $\alpha$-mixing stochastic process over a finite but potentially large state space. We consider the problem of estimating the probability mass placed by the stationary…

The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…

In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…

We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on…

We theoretically evaluate the impact of drift-free noise on the dynamics of $\mathcal{PT}$-symmetric non-Hermitian systems with an exceptional point, which have recently been proposed for sensors. Such systems are currently considered as…

This paper deals with the intersection point process of a stationary and isotropic Poisson hyperplane process in $\mathbb{R}^d$ of intensity $t>0$, where only hyperplanes that intersect a centred ball of radius $R>0$ are considered. Taking…

Let $\{\eta_i\}_{i\ge 1}$ be a sequence of dependent Bernoulli random variables. While the Poisson approximation for the distribution of $\sum_{i=1}^n\eta_i$ has been extensively studied in the literature, this paper establishes new…

Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise…

Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…

Correlation spectroscopy has been proposed as a spectroscopic technique for measuring the coherence between the ground states in electromagnetically induced transparency (EIT). While in time domain the steep dispersion in EIT condition…

We study a Dirichlet--Ferguson process $\zeta$ on a general phase space. First we reprove the chaos expansion from Peccati (2008), providing an explicit formula for the kernel functions. Then we proceed with developing a Malliavin calculus…

The scale-invariant spacings lemma due to Arratia, Barbour and Tavar{\'e} establishes the distributional identity of a self-similar Poisson process and the set of spacings between the points of this process. In this note we connect this…

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for…

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, $N$. When the advection term in Vlasov…

This paper studies the first hitting times of generalized Poisson processes $N^f(t)$, related to Bernstein functions $f$. For the space-fractional Poisson processes, $N^\alpha(t)$, $t>0$ (corresponding to $f= x^\alpha$), the hitting…

We introduce a continuum percolation model defined on the points of a d-dimensional homogeneous Poisson process. Each Poisson point is connected to all points within its connection range, which depends on the distances to the other Poisson…

Spectral methods are well suited for solving hydrodynamic problems in which the self-gravity of the flow needs to be considered. Because Poisson's equation is linear, the numerical solution for the gravitational potential for each…

We extend the Heston stochastic volatility model to a Hilbert space framework. The tensor Heston stochastic variance process is defined as a tensor product of a Hilbert-valued Ornstein-Uhlenbeck process with itself. The volatility process…

We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…

Arranging many modules within a bounded domain without overlap, central to the Electronic Design Automation (EDA) of very large-scale integrated (VLSI) circuits, represents a broad class of discrete geometric optimization problems with…