Exponential inequalities and functional central limit theorems for random fields

We prove a modified logarithmic Sobolev inequalities, a Stein inequality and an exact fourth moment theorem for a large class of point processes including mixed binomial processes

Roughly speaking functional central limit theorems hold true as soon as the self-intersection local time of the random walk converges almost surely to some constant.. To be com-

in the (much simpler) case of random fields defined on the circle [19], Section 3, the condi- tions for the central limit theorem could be expressed in terms of convolutions of

Actually, the limit analysis of the autocorrelation and distributions of the M -DWPT coefficients is more intricate than presented in [1] and [3] because, as shown below, this

Motivated by random evolutions which do not start from equilibrium, in a recent work, Peligrad and Voln´ y (2018) showed that the central limit theorem (CLT) holds for

Key words and phrases: Central limit theorem, spatial processes, m- dependent random fields, weak mixing..

In the context of this work, we consider functionals which act on these clusters of relevant values and we develop useful lemmas in order to simplify the essential step to establish

exponential Young funtions for stationary real random elds whih are bounded.. or satisfy some nite exponential