Invariance principle for stochastic processes with short memory

Details Invariance principle for stochastic processes with short memory Invariance principle for stochastic processes with short memory

2006-12-22

arxiv.org/abs/math/0612707v1

IMS Lecture Notes Monograph Series 2006, Vol. 51, 18-32

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000734 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921706000000734

In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the weak invariance principle for partial sums of linear processes with short memory. We prove that whenever the partial sums of innovations satisfy the $L_p$--invariance principle, then so does the partial sums of its corresponding linear process.

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