Empirical Quantile Central Limit Theorems for Some Self-Similar Processes

James Kuelbs () and Joel Zinn ()
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James Kuelbs: University of Wisconsin
Joel Zinn: Texas A&M University

Journal of Theoretical Probability, 2015, vol. 28, issue 1, 313-336

Abstract: Abstract In Swanson (Probab Theory Relat Fields 138:269–304, 2007), a central limit theorem (CLT) for the sample median of independent Brownian motions with value $$0$$ 0 at $$0$$ 0 was proved. Here, we extend this result in two ways. We prove such a result for a collection of self-similar processes which include the fractional Brownian motions, all stationary, independent increment symmetric stable processes tied down at 0 as well as iterated and integrated Brownian motions. Second, our results hold uniformly over all quantiles in a compact sub-interval of (0,1). We also examine sample function properties connected with these CLTs.

Keywords: Central limit theorems; Empirical processes; Empirical quantile processes; Self-similar processes; Primary 60F05; Secondary 60F17; 62E20 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-013-0511-2

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