2013/08/20 by James Kuelbs, Kuelbs, James, Joel Zinn +1
Economics, Econometrics and Finance · Mathematics · #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Stochastic processes and financial applications #math.PR #math.ST #msc:60F05 #msc:60F17 #msc:62E20 #stat.TH
paper · pdf · doi:10.48550/arxiv.1308.4194
24 pages. arXiv admin note: text overlap with arXiv:1111.4591
arxiv created 2013/08/20 · arxiv updated 2013/08/21
In a paper of Jason Swanson, a CLT for the sample median of independent Brownian motions with value 0 at 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.