### Invariance principle for stochastic processes with short memory

#### Abstract

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.

First Page:
Primary Subjects: 60F17, 60F17
Secondary Subjects: 60K99, 60G48, 60G10
Keywords: stationary process; linear processes; Brownian motion; invariance principle; weakly dependent sequences
Full-text: Open access