Related papers: On the almost sure central limit theorem for ARX p…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
Ordered pivotal sampling is one of the simplest algorithm to perform without-replacement unequal probability sampling. It has found uses in the context of longitudinal surveys and spatial sampling, and enables in particular a good spatial…
We obtain strong invariance principles for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu/2}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…
We propose a post-hoc adaptive conformal anomaly detection method for monitoring time series that leverages predictions from pre-trained foundation models without requiring additional fine-tuning. Our method yields an interpretable anomaly…
We prove a central limit theorem for stationary multiple (random) fields of martingale differences $f\circ T_{\underline{i}}$, $\underline{i}\in \Bbb Z^d$, where $T_{\underline{i}}$ is a $\Bbb Z^d$ action. In most cases the multiple…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
This paper presents a novel robust predictive controller for constrained nonlinear systems that is able to track piece-wise constant setpoint signals. The tracking model predictive controller presented in this paper extends the nonlinear…
This is an expository review paper elaborating on the proof of the martingale functional central limit theorem (FCLT). This paper also reviews tightness and stochastic boundedness, highlighting one-dimensional criteria for tightness used in…
The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…
In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable.…
In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak-Ruppert averaged iterates generated by the asynchronous Q-learning algorithm with a polynomial stepsize $k^{-\omega},\, \omega \in (1/2,…
Based on Pontryagin Maximum Principle (PMP), this paper establishes a generalized PMP aiming at control system with with extra input/output terms. The paper details the adaptive target and gives a proof of the generalized theorem.…
Statistical procedures rarely retain all features of the observed data. A sufficient statistic removes information irrelevant to a parameter; a maximum likelihood estimate compresses an empirical objective into an optimizing point; and a…
Inference is a main task in structured prediction and it is naturally modeled with a graph. In the context of Markov random fields, noisy observations corresponding to nodes and edges are usually involved, and the goal of exact inference is…
In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
The modified massive Arratia flow is a model for the dynamics of passive particle clusters moving in a random fluid that accounts for the effects of mass aggregation. We show a central limit theorem for the point process associated to the…