Another Pairwise Independent, Stationary Chain

James B. Robertson
Additional contact information
James B. Robertson: University of California, Department of Statistics and Applied Probability

A chapter in Approximation, Probability, and Related Fields, 1994, pp 423-434 from Springer

Abstract: Abstract We construct a pairwise independent, stationary chain {X n:n=1,2,...} such that $$P\left\{ {{X_n} = 1} \right\} = P\left\{ {{X_n} = - 1} \right\} = \frac{1}{2}{\text{ }}E\left[ {{X_1}{X_2}{X_3}} \right] = - E\left[ {{X_1}{X_3}{X_5}} \right] = \frac{1}{2}.$$ and E[X 1 X 2 X 3]_= -E[X1X3X5]_= 1/2. The properties of this chain are also studied. In particular it is shown that the chain is ergodic but not weakly mixing.

Keywords: Primary; 60G10; secondary; 58F11; ergodic; mixing; third moments; embedding (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-2494-6_33

Ordering information: This item can be ordered from
http://www.springer.com/9781461524946

DOI: 10.1007/978-1-4615-2494-6_33

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().