Convergence of functionals of sums of r.v.s to local times of fractional stable motions.

DOI10.1214/009117904000000658zbMath1049.60019arXivmath/0410097OpenAlexW3102096883MaRDI QIDQ1878981

P. Jeganathan

Publication date: 15 September 2004

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0410097

zbMATH Keywords

fractional Brownian motionlocal timeARIMAheavy tailed distributionsfractional stable motionfunctional of sumweak convergence to local times

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Central limit and other weak theorems (60F05) General nonlinear regression (62J02) Self-similar stochastic processes (60G18) Local time and additive functionals (60J55)

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Cites Work

• Limit theorems for sums of linearly generated random variables
• Weighted sums of i.i.d. random variables attracted to integrals of stable processes
• Comportement asymptotique du temps d'occupation du processus des sommes partielles. (Asymptotical behavior of the occupation time of partial sums)
• ASYMPTOTICS FOR NONLINEAR TRANSFORMATIONS OF INTEGRATED TIME SERIES
• Nonlinear Regressions with Integrated Time Series
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