Related papers: Invariance principle for stochastic processes with…

In this note, we prove a conditionally centered version of the quenched weak invariance principle under the Hannan condition, for stationary processes. In the course, we obtain a (new) construction of the fact that any stationary process…

In causal models, a given mechanism is assumed to be invariant to changes of other mechanisms. While this principle has been utilized for inference in settings where the causal variables are observed, theoretical insights when the variables…

We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…

Long Memory Stochastic volatility (LMSV) models capture two standardized features of financial data: the log-returns are uncorrelated, but their squares, or absolute values are (highly) dependent and they may have heavy tails. EGARCH and…

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…

The classical Donsker weak invariance principle is extended to a Besov spaces framework. Polygonal line processes build from partial sums of stationary martingale differences as well independent and identically distributed random variables…

The objective of this paper is to prove a functional weak invariance principle for a local time of a process of the form $X_{n}=\varphi\circ T^{n}$ where $\left(X,\mathcal{B},T,m\right)$ is a measure preserving system with a transfer…

Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by…

One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics,…

Based on deleting-item central limit theory, the classical Donsker's theorem of partial-sum process of independent and identically distributed (i.i.d.) random variables is extended to incomplete partial-sum process. The incomplete…

Most work on the verification of concurrent objects for shared memory assumes sequential consistency, but most multicore processors support only weak memory models that do not provide sequential consistency. Furthermore, most verification…

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These…

In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…

This note investigates invariance principles for sums of N(nt) iid radom variables, where n is an integer, t is a positive real number and N(u) is a stochastic process with nonnegative integer values. We show that the sequence of sums of…

Donsker's invariance principle is shown to hold for random walks in rough path topology. As application, we obtain Donsker-type weak limit theorems for stochastic integrals and differential equations.

This paper is devoted to establish an invariance principle where the limit process is a multifractional Gaussian process with a multifractional function which takes its values in $(1/2,1)$. Some properties, such as regularity and local…

We consider a field $f \circ T_1^{i_1} \circ \cdots \circ T_d^{i_d}$ where $T_1, \dots , T_d$ arecommuting transformations, one of them at least being ergodic. Considering the case of commuting filtrations, we are interested by giving…

We establish almost sure invariance principles, a strong form of approximation by Brownian motion, for non-stationary time-series arising as observations on dynamical systems. Our examples include observations on sequential expanding maps,…

We investigate the invariance principle for set-indexed partial sums of a stationary field $(X\_{k})\_{k\in\mathbb{Z}^{d}}$ of martingale-difference or independent random variables under standard-normalization or self-normalization…