Strong invariance principle for dependent random fields
نویسنده
چکیده
A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, with the estimate of the convergence rate in the CLT for random fields under consideration.
منابع مشابه
A Nonconventional Invariance Principle for Random Fields
In [16] we obtained a nonconventional invariance principle (functional central limit theorem) for sufficiently fast mixing stochastic processes with discrete and continuous time. In this paper we derive a nonconventional invariance principle for sufficiently well mixing random fields.
متن کاملA Strong Invariance Principle for Associated Random Fields ? ?
In this paper we generalize Yu’s [Ann. Probab. 24 (1996) 2079–2097] strong invariance principle for associated sequences to the multiparameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n → ∞. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15–37] multi-parameter blocking technique, the Csörgő ...
متن کاملThe quenched invariance principle for random walks in random environments admitting a bounded cycle representation
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields 129 (2004) 219– 244) to the non-reversible setting. Résumé. Nous dérivons un principe d’in...
متن کاملAlmost Sure Invariance Principle for Random Piecewise Expanding Maps
The objective of this note is to prove the almost sure invariance principle (ASIP) for a large class of random dynamical systems. The random dynamics is driven by an invertiblemeasure preserving transformation σ of (Ω,F ,P) called the base transformation. Trajectories in the phase space X are formed by concatenations f ω := fσn−1ω ◦ · · · ◦ fσω ◦ fω of maps from a family of maps fω : X → X, ω ∈...
متن کاملBallistic Random Walk in a Random Environment with a Forbidden Direction
We consider a ballistic random walk in an i.i.d. random environment that does not allow retreating in a certain fixed direction. Homogenization and regeneration techniques combine to prove a law of large numbers and an averaged invariance principle. The assumptions are non-nestling and 1 + ε (resp. 2 + ε) moments for the step of the walk uniformly in the environment, for the law of large number...
متن کامل