Related papers: Correction. Strong invariance principles for seque…

This is a brief pedagogical introduction to the theory of large deviations. It appeared in the ICTS Newsletter 2017 (Volume 3, Issue 2), goo.gl/pZWA6X.

We improve a known result on the strong consistency of M-estimates of the regression parameters in a linear model for independent and identically distributed random errors under some mild conditions.

We consider a measure of dependence for symmetric $\alpha$-stable random vectors, which was introduced by the author in 1976. We demonstrate that this measure of dependence can be extended for much more broad class of random vectors (up to…

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…

This article generalises the concept of realised covariation to Hilbert-space-valued stochastic processes. More precisely, based on high-frequency functional data, we construct an estimator of the trace-class operator-valued integrated…

We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…

Rejoinder of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].

We consider generalized Bayesian inference on stochastic processes and dynamical systems with potentially long-range dependency. Given a sequence of observations, a class of parametrized model processes with a prior distribution, and a loss…

In this paper, the Bahadur representation of sample quantiles based on associated sequences is established under polynomially decaying of covariances. The rate of approximation depends on the covariances decay degree and becomes close to…

This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999), we measure the strength of dependence by covariances of nonlinearly…

We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…

Using changes of probability measure developed by \mbox{Grama} and Haeusler (Stochastic Process.\ Appl., 2000), we obtain two generalizations of the deviation inequalities of Lanzinger and Stadtm\"{u}ller (Stochastic Process.\ Appl., 2000)…

In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian…

We establish a large deviation principle for the trajectories of Wiener processes subject to random resets to the origin occurring according to a Poisson process. In addition to the pathwise large deviation principle, we identify the rate…

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…

The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall, Jing and Lahiri (1998) on functionals of Gaussian processes and Nordman and Lahiri (2005) on linear processes. In…

Corrected confidence intervals are developed for the mean of the second component of a bivariate normal process when the first component is being monitored sequentially. This is accomplished by constructing a first approximation to a…

Stochastic point processes relevant to the theory of long-range aperiodic order are considered that display diffraction spectra of mixed type, with special emphasis on explicitly computable cases together with a unified approach of…

Results have been moved to a published article, see arXiv:0812.2669v4[math.PR]

Predicting multivariate time series is crucial, demanding precise modeling of intricate patterns, including inter-series dependencies and intra-series variations. Distinctive trend characteristics in each time series pose challenges, and…