Related papers: Weak convergence of Vervaat and Vervaat Error proc…
The weak value approximation has been in use for thirty-five years, but it has not as of yet received a truly complete derivation, leaving its mathematical validity in a state of limbo. Herein, I fill this gap, deriving the weak value…
In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…
We study the closure of approximating sequences of some diffusion equations under certain weak convergence. A specific description of the closure under weak $H^1$-convergence is given, which reduces to the original equation when the…
Notions of weak and uniformly weak mixing (to zero) are defined for bounded sequences in arbitrary Banach spaces. Uniformly weak mixing for vector sequences is characterized by mean ergodic convergence properties. For bounded sequences,…
We analyze the ordinal structure of long-range dependent time series. To this end, we use so called ordinal patterns which describe the relative position of consecutive data points. We provide two estimators for the probabilities of ordinal…
Concerning bivariate least squares linear regression, the classical approach pursued for functional models in earlier attempts is reviewed using a new formalism in terms of deviation (matrix) traces. Within the framework of classical error…
The proofs of K. Oka's Coherence Theorems are based on Weierstrass' Preparation (division) Theorem. Here we formulate and prove a Weak Coherence Theorem without using Weierstrass' Preparation Theorem, but only with power series expansions:…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
We consider numerical approximations of stochastic Langevin equations by implicit methods. We show a weak backward error analysis result in the sense that the generator associated with the numerical solution coincides with the solution of a…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
In this research note, we show the relationship between two non-admissible argumentation framework semantics: cogent and weakly admissible semantics. We prove that, while cogent extensions are weakly admissible, the converse is not true.
We propose a weak-identification-robust test for linear instrumental variable (IV) regressions with high-dimensional instruments, whose number is allowed to exceed the sample size. In addition, our test is robust to general error…
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…
We use the martingale convergence method to get the weak convergence theorem on general functionals of partial sums of independent heavy-tailed random variables. The limiting process is the stochastic integral driven by $\alpha-$stable…
Let $X$ be a L\'evy process with regularly varying L\'evy measure $\nu$. We obtain sample-path large deviations for scaled processes $\bar X_n(t) \triangleq X(nt)/n$ and obtain a similar result for random walks. Our results yield detailed…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
A central limit theorem with explicit error bound, and a large deviation result are proved for a sequence of weakly dependent random variables of a special form. As a corollary, under certain conditions on the function $f: [0,1] \to…
Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined for abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is…
The paper studies the rate of convergence of the weak Euler approximation for solutions to SDEs driven by Levy processes, with Hoelder-continuous coefficients. It investigates the dependence of the rate on the regularity of coefficients and…