Related papers: U-statistics in stochastic geometry

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…

The purpose of the present paper is to establish explicit bounds on moderate deviation probabilities for a rather general class of geometric functionals enjoying the stabilization property, under Poisson input and the assumption of a…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Malliavin calculus provides a characterization of the centered model in regularity structures that is stable under removing the small-scale cut-off. In conjunction with a spectral gap inequality, it yields the stochastic estimates of the…

We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…

We prove a convergence theorem for U-statistics of degree two, where the data dimension $d$ is allowed to scale with sample size $n$. We find that the limiting distribution of a U-statistic undergoes a phase transition from the…

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…

Given $n$ independent random marked $d$-vectors (points) $X_i$ distributed with a common density, define the measure $\nu_n=\sum_i\xi_i$, where $\xi_i$ is a measure (not necessarily a point measure) which stabilizes; this means that $\xi_i$…

Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…

It is considered Ornstein-Uhlenbeck process $ x_t = x_0 e^{-\theta t} + \mu (1-e^{-\theta t}) + \sigma \int_0^t e^{-\theta (t-s)} dW_s$, where $x_0 \in R$, $\theta>0$, $ \mu \in R$ and $\sigma > 0$ are parameters. By use values $(z_k)_{k…

In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…

Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random…

The Malliavin integration-by-parts formula is a key ingredient to develop stochastic analysis on the Wiener space. In this article we show that a suitable integration-by-parts formula also characterizes a wide class of Gaussian processes,…

We introduce a new class of numerical schemes which allow for low regularity approximations to the expectation $ \mathbb{E}(|u_{k}(\tau, v^{\eta})|^2)$, where $u_k$ denotes the $k$-th Fourier coefficient of the solution $u$ of the…

In this article we obtain concentration inequalities for Poisson $U$-statistics $F_m(f,\eta)$ of order $m\ge 1$ with kernels $f$ under general assumptions on $f$ and the intensity measure $\gamma \Lambda$ of underlying Poisson point process…

We describe stochastic calculus in the context of processes that are driven by an adapted point process of locally finite intensity and are differentiable between jumps. This includes Markov chains as well as non-Markov processes. By…

We study the distribution of large prime factors of a random element $u$ of arithmetic sequences satisfying simple regularity and equidistribution properties. We show that if such an arithmetic sequence has level of distribution $1$ the…

We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…

Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here…