## Institute of Mathematical Statistics Lecture Notes - Monograph Series

- Lecture Notes--Monograph Series
- Number 51, 2006, 18-32

### Invariance principle for stochastic processes with short memory

Magda Peligrad and Sergey Utev

#### 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.

#### Chapter information

**Source***High Dimensional Probability: Proceedings of the Fourth International Conference* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006)

**Dates**

First available in Project Euclid: 28 November 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.lnms/1196284101

**Digital Object Identifier**

doi:10.1214/074921706000000734

**Mathematical Reviews number (MathSciNet)**

MR2387758

**Zentralblatt MATH identifier**

1122.60038

**Subjects**

Primary: 60F17: Functional limit theorems; invariance principles 60F17: Functional limit theorems; invariance principles

Secondary: 60K99: None of the above, but in this section 60G48: Generalizations of martingales 60G10: Stationary processes

**Keywords**

stationary process linear processes Brownian motion invariance principle weakly dependent sequences

**Rights**

Copyright © 2006, Institute of Mathematical Statistics

#### Citation

Peligrad, Magda; Utev, Sergey. Invariance principle for stochastic processes with short memory. High Dimensional Probability, 18--32, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000734. https://projecteuclid.org/euclid.lnms/1196284101