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Some Invariance Principles

In: Markov Chains

Author

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  • David Freedman

    (University of California, Department of Statistics)

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).

Suggested Citation

  • David Freedman, 1983. "Some Invariance Principles," Springer Books, in: Markov Chains, chapter 3, pages 82-110, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5500-0_3
    DOI: 10.1007/978-1-4612-5500-0_3
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