Related papers: Martingale approximations for sums of stationary p…
We provide a framework for empirical process theory of locally stationary processes using the functional dependence measure. Our results extend known results for stationary Markov chains and mixing sequences by another common possibility to…
We consider a random walk on $\R^d$ in a polynomially mixing random environment that is refreshed at each time step. We use a martingale approach to give a necessary and sufficient condition for the almost-sure functional central limit…
We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
The martingale method is used to establish concentration inequalities for a class of dependent random sequences on a countable state space, with the constants in the inequalities expressed in terms of certain mixing coefficients. Along the…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+\infty)$ for such CB processes. We give a representation of the…
The G\"artner-Ellis condition for the square of an asymptotically stationary Gaussian process is established. The same limit holds for the conditional distri-bution given any fixed initial point, which entails weak multiplicative…
In this paper, we give estimates of the minimal ${\mathbb{L}}^1$ distance between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary sequences satisfying projective criteria in the style of…
We establish sufficient conditions for the asymptotic normality of kernel density estimators, applied to causal linear random fields. Our conditions on the coefficients of linear random fields are weaker than known results, although our…
We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…
We define a compact version of the Hilbert transform, which we then use to write explicit expressions for the partial sums and remainders of arbitrary Fourier series. The expression for the partial sums reproduces the known result in terms…
The paper is a sketch of systematic presentation of distributional limit theorems and their refinements for compound sums. When analyzing, e.g., ergodic semi-Markov systems with discrete or continuous time, this allows us to separate those…
We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…
By application of the theory for second-order linear differential equations with two turning points developed in \cite{Olver1975}, uniform asymptotic approximations are obtained for the Lam\'{e} and Mathieu functions with a large real…
The first aim of this paper is to wonder to what extent we can generalize the central limit theorem of Gordin [5] under the so-called L 1-projective criteria to ergodic stationary random fields when completely commuting filtrations are…
A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some…
Statistical inference for non-stationary data is hindered by the failure of classical central limit theorems (CLTs), not least because there is no fixed Gaussian limit to converge to. To resolve this, we introduce relative weak convergence,…
In this paper, we establish a version of the central limit theorem for Markov-Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bounded-Lipschitz distance and enjoy a continuous form of the…