# The empirical process of a short-range dependent stationary sequence under Gaussian subordination

@inproceedings{Cs2005TheEP, title={The empirical process of a short-range dependent stationary sequence under Gaussian subordination}, author={Sfindor Cs and Jan Mielnicznk}, year={2005} }

- Published 2005

Consider the stationary sequence X1 = G(Z1), X2 = G(Z2), . . . , where G( 9 ) is an arbitrary Borel function and Z1,Z2,... is a mean-zero stationary Gaussian sequence with covariance function r(k)= E(Z1Zk+I) satisfying r(0) = 1 and E ~1 I r ( k ) l m < oc, where, with I{ 9 } denoting the indicator function and F ( 9 ) the continuous marginal distribution function of the sequence {X~}, the integer m is the Hermite rank o f the family {I{G( ) -< x} F (x ) : x C IR}. Let Fn( 9 ) be the empiricalâ€¦Â CONTINUE READING

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#### References

##### Publications referenced by this paper.

Showing 1-10 of 13 references

## The empirical process of some long-range dependent sequences with an application to U-statistics

View 9 Excerpts

Highly Influenced

## CLT and other limit theorems for fimctionals of Ganssian processes

View 7 Excerpts

Highly Influenced

## Central limit theorems for non-linear ftmctionals of Gaussian fields

View 6 Excerpts

Highly Influenced

## Convergence of integrated processes of arbitrary Hermite rank

View 6 Excerpts

Highly Influenced

## Non-central limit theorems for non-linear functionals of Gaussian fields

View 5 Excerpts

Highly Influenced

## Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence

View 7 Excerpts

Highly Influenced

## The asymptotic distribution theory of the empiric cdf for mixing stochastic processes

View 4 Excerpts

Highly Influenced

## A note on empirical processes of strong-mixing sequences

View 4 Excerpts

Highly Influenced

## A note on weak convergence of empirical processes for sequences of qS-mixing random variables

View 4 Excerpts

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## Convergence of probability measures

View 7 Excerpts

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