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We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....
We establish new exponential inequalities for partial sums of random fields. Next, using classical
chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of
sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the
condition is expressed in terms of a series of conditional expectations. For non-uniform -mixing
random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients.
...
We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit. We also discuss...
In this paper, we give estimates of the minimal distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.
We continue the investigation started in a previous paper, on
weak convergence to infinitely divisible distributions with finite
variance. In the present paper, we study this problem for some
weakly dependent random variables, including in particular
associated sequences. We obtain minimal conditions expressed in
terms of individual random variables. As in the i.i.d. case, we
describe the convergence to the Gaussian and the purely
non-Gaussian parts of the infinitely divisible limit. We also
discuss...
Considering the centered empirical distribution function
as
a variable in , we derive non asymptotic upper
bounds for the deviation of the -norms of
as well as central limit theorems for the empirical process
indexed by the elements of generalized Sobolev balls. These results
are valid for a large class of dependent sequences, including
non-mixing processes and some dynamical systems.
In this paper we study the almost sure conditional central limit theorem in its functional form for a class of random variables satisfying a projective criterion. Applications to strongly mixing processes and nonirreducible Markov chains are given. The proofs are based on the normal approximation of double indexed martingale-like sequences, an approach which has interest in itself.
Consider an autoregressive model with measurement error: we observe
=
+
, where the unobserved
is a stationary solution of the autoregressive equation
=
(
) +
. The regression function
is known up to a finite dimensional parameter
to be estimated. The distributions of
and
are unknown and
...
In this paper we derive the moderate deviation principle for stationary sequences of bounded random variables under martingale-type conditions. Applications to functions of -mixing sequences, contracting Markov chains, expanding maps of the interval, and symmetric random walks on the circle are given.
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