Geodesic
Decay rate of iterated integrals of branched rough paths
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 945-969

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Iterated integrals of paths arise frequently in the study of the Taylor's expansion for controlled differential equations. We will prove a factorial decay estimate, conjectured by M. Gubinelli, for the iterated integrals of non-geometric rough paths. We will explain, with a counter example, why the conventional approach of using the neoclassical inequality fails. Our proof involves a concavity estimate for sums over rooted trees and a non-trivial extension of T. Lyons' proof in 1994 for the factorial decay of iterated Young's integrals.

DOI : 10.1016/j.anihpc.2017.09.002
Keywords: Branched rough paths, Non-geometric rough paths, Iterated integrals 
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     title = {Decay rate of iterated integrals of branched rough paths},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {945--969},
     publisher = {Elsevier},
     volume = {35},
     number = {4},
     year = {2018},
     doi = {10.1016/j.anihpc.2017.09.002},
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     zbl = {1391.60122},
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Boedihardjo, Horatio. Decay rate of iterated integrals of branched rough paths. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 945-969. doi: 10.1016/j.anihpc.2017.09.002

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