On the strong approximation and functional limit laws for the increments of the non-overlapping k-spacings processes

2006/06/24 by Salim Bouzebda, Bouzebda, Salim, Nabil Nessigha +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Statistics Theory (math.ST) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.0807.3868

openalex publication_date 2008/07/24 · openalex created_date 2020/05/13 · openalex updated_date 2026/07/28

Abstract

The first aim of the present paper, is to establish strong approximations of the uniform non-overlapping k-spacings process extending the results of Aly et al. (1984). Our methods rely on the invariance principle in Mason and van Zwet (1987). The second goal, is to generalize the Dindar (1997) results for the increments of the spacings quantile process to the uniforme non-overlapping k-spacings quantile process. We apply the last result to characterize the limit laws of functionals of the increments k-spacings quantile process.

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