Related papers: Modified empirical CLT's under only pre-Gaussian c…
Many control tasks can be formulated as a tracking problem of a known or unknown reference signal. Examples are movement compensation in collaborative robotics, the synchronisation of oscillations for power systems or reference tracking of…
Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
We obtain several extensions of Talagrand's lower bound for the small deviation probability using metric entropy. For Gaussian processes, our investigations are focused on processes with sub-polynomial and, respectively, exponential…
We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or $\beta$-ensembles. We use a method based on a change of variables which allows to treat fairly general situations, including multi-cut and, for the…
Model predictive control allows to provide high performance and safety guarantees in the form of constraint satisfaction. These properties, however, can be satisfied only if the underlying model, used for prediction, of the controlled…
We present a very simple yet powerful generalization of a previously described model and algorithm for estimation of multiple dipoles from magneto/electro-encephalographic data. Specifically, the generalization consists in the introduction…
It is well known that central order statistics exhibit a central limit behavior and converge to a Gaussian distribution as the sample size grows. This paper strengthens this known result by establishing an entropic version of the CLT that…
We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…
Conditioning Markov processes to avoid a set is a classical problem that has been studied in many settings. In the present article we study the question if a Levy process can be conditioned to avoid an interval and, if so, the path behavior…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
Gaussian processes are a powerful class of non-linear models, but have limited applicability for larger datasets due to their high computational complexity. In such cases, approximate methods are required, for example, the recently…
This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…
Brian Pitts has recently claimed to show via straightforward calculation that, at least in the case of Hamiltonian electromagnetism, an arbitrary first-class constraint ``generates not a gauge transformation, but a bad physical change''…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
The article presents a systematic study of the problem of conditioning a Gaussian random variable $\xi$ on nonlinear observations of the form $F \circ \phi(\xi)$ where $\phi: \mathcal{X} \to \mathbb{R}^N$ is a bounded linear operator and…
We establish a central limit theorem for the unnormalized linear statistic of the Gaussian Unitary Ensemble under optimal conditions: the linear statistics converges if and only if the expression for the limiting variance is finite.
Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a…
We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…
We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing…