Abstract
This chapter deals with the asymptotic behavior of the partial sums of functionals of a Markov chain, and in part is an explanation of the central limit theorem for these processes. Markov (1906) introduced his chains in order to extend the central limit theorem; this chapter continues his program. Section 3 contains an arcsine law for functional processes. The invariance principles of Donsker (1951) and Strassen (1964), to be discussed in B & D, are extended to functional processes in Section 4. For an alternative treatment of some of these results, see (Chung, 1960, Section I.16).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1983 David A. Freedman
About this chapter
Cite this chapter
Freedman, D. (1983). Some Invariance Principles. In: Markov Chains. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5500-0_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-5500-0_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-5502-4
Online ISBN: 978-1-4612-5500-0
eBook Packages: Springer Book Archive