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November 2008 A tree approach to p-variation and to integration
Jean Picard
Ann. Probab. 36(6): 2235-2279 (November 2008). DOI: 10.1214/07-AOP388


We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of p-variation of the path, and integration with respect to the path. In particular, the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include some stochastic paths such as martingales, Lévy processes and fractional Brownian motions (for which an estimator of the Hurst parameter is given).


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Jean Picard. "A tree approach to p-variation and to integration." Ann. Probab. 36 (6) 2235 - 2279, November 2008.


Published: November 2008
First available in Project Euclid: 19 December 2008

zbMATH: 1157.60055
MathSciNet: MR2478682
Digital Object Identifier: 10.1214/07-AOP388

Primary: 26A42 , 60G17 , 60H05

Keywords: fractional Brownian motion , Lebesgue–Stieltjes integrals , Lévy processes , Real trees , Rough paths , variations of paths

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 6 • November 2008
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