arXiv math/06127072006-12-22math.PR

Invariance principle for stochastic processes with short memory

Magda Peligrad, Sergey Utev

备注：: Published at http://dx.doi.org/10.1214/074921706000000734 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: IMS Lecture Notes Monograph Series 2006, Vol. 51, 18-32
DOI：: 10.1214/074921706000000734

英文摘要：

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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