Law of the Iterated Logarithm for U-Statistics of Weakly Dependent Observations [PDF]
, 2009 The law of the iterated logarithm for partial sums of weakly dependent processes was intensively studied by Walter Philipp in the late 1960s and 1970s. In this paper, we aim to extend these results to nondegenerate U-statistics of data that are strongly ...
Dehling, Herold, Wendler, Martin
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Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas [PDF]
, 2020 In this paper, we show how the Gordin martingale approximation method fits into the anisotropic Banach space framework. In particular, for the time-one map of a finite horizon planar periodic Lorentz gas, we prove that Holder observables satisfy ...
Demers, Mark +2 more
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On martingale approximations and the quenched weak invariance principle [PDF]
, 2012 In this paper, we obtain sufficient conditions in terms of projective criteria under which the partial sums of a stationary process with values in ${\mathcal{H}}$ (a real and separable Hilbert space) admits an approximation, in ${\mathbb{L}}^p({\mathcal ...
Cuny, Christophe, Merlevède, Florence
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A strong invariance principle for associated random fields [PDF]
, 2005 In this paper we generalize Yu's [Ann. Probab. 24 (1996) 2079-2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n\to \infty.
Balan, Raluca M.
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Law of the iterated logarithm for stationary processes [PDF]
, 2007 There has been recent interest in the conditional central limit question for (strictly) stationary, ergodic processes $...,X_{-1},X_0,X_1,...$ whose partial sums $S_n=X_1+...+X_n$ are of the form $S_n=M_n+R_n$, where $M_n$ is a square integrable ...
Woodroofe, Michael, Zhao, Ou
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Invariance Principle for the Random Conductance Model with dynamic bounded Conductances [PDF]
, 2012 We study a continuous time random walk X in an environment of dynamic random conductances. We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched
Andres, Sebastian
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Invariance principles for random walks conditioned to stay positive [PDF]
, 2008 Let $\{S_n\}$ be a random walk in the domain of attraction of a stable law $\mathcal{Y}$, i.e. there exists a sequence of positive real numbers $(a_n)$ such that $S_n/a_n$ converges in law to $\mathcal{Y}$.
Caravenna, Francesco, Chaumont, Loïc
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On the functional CLT for stationary Markov Chains started at a point
, 2016 We present a general functional central limit theorem started at a point also known under the name of quenched. As a consequence, we point out several new classes of stationary processes, defined via projection conditions, which satisfy this type of ...
Barrera, David +2 more
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Multidimensional limit theorems for homogeneous sums: a general transfer principle [PDF]
, 2015 The aim of the present paper is to establish the multidimensional counterpart of the \textit{fourth moment criterion} for homogeneous sums in independent leptokurtic and mesokurtic random variables (that is, having positive and zero fourth cumulant ...
Nourdin, Ivan +3 more
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Rates of convergence in the strong invariance principle under projective criteria [PDF]
, 2012 We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence.
Dedecker, Jérôme +2 more
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