@article{Cass:2017:10.1214/16-AOP1117,
author = {Cass, T and Ogrodnik, M},
doi = {10.1214/16-AOP1117},
journal = {Annals of Probability},
pages = {2477--2504},
title = {Tail estimates for Markovian rough paths},
url = {http://dx.doi.org/10.1214/16-AOP1117},
volume = {45},
year = {2017}
}

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TY  - JOUR
AB  - The accumulated local p-variation functional [Ann. Probab. 41 (213) 3026–3050] arises naturally in the theory of rough paths in estimates both for solutions to rough differential equations (RDEs), and for the higher-order terms of the signature (or Lyons lift). In stochastic examples, it has been observed that the tails of the accumulated local p-variation functional typically decay much faster than the tails of classical p-variation. This observation has been decisive, for example, for problems involving Malliavin calculus for Gaussian rough paths [Ann. Probab. 43 (2015) 188–239].All of the examples treated so far have been in this Gaussian setting that contains a great deal of additional structure. In this paper, we work in the context of Markov processes on a locally compact Polish space E, which are associated to a class of Dirichlet forms. In this general framework, we first prove a better-than-exponential tail estimate for the accumulated local p-variation functional derived from the intrinsic metric of this Dirichlet form. By then specialising to a class of Dirichlet forms on the step ⌊p⌋ free nilpotent group, which are sub-elliptic in the sense of Fefferman–Phong, we derive a better than exponential tail estimate for a class of Markovian rough paths. This class includes the examples studied in [Probab. Theory Related Fields 142 (2008) 475–523]. We comment on the significance of these estimates to recent papers, including the results of Ni Hao [Personal communication (2014)] and Chevyrev and Lyons [Ann. Probab. To appear].
AU  - Cass,T
AU  - Ogrodnik,M
DO  - 10.1214/16-AOP1117
EP  - 2504
PY  - 2017///
SN  - 0091-1798
SP  - 2477
TI  - Tail estimates for Markovian rough paths
T2  - Annals of Probability
UR  - http://dx.doi.org/10.1214/16-AOP1117
UR  - http://hdl.handle.net/10044/1/31712
VL  - 45
ER  - 

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