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A moment estimate of the derivative process in rough path theory


Author: Yuzuru Inahama
Journal: Proc. Amer. Math. Soc. 140 (2012), 2183-2191
MSC (2010): Primary 60H10; Secondary 60G99
DOI: https://doi.org/10.1090/S0002-9939-2011-11051-7
Published electronically: October 11, 2011
MathSciNet review: 2888204
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Abstract: In this paper we prove that the derivative process of a rough differential equation driven by a Brownian rough path has finite $ L^r$-moment for any $ r \ge 1$. This kind of problem is easy in the usual SDE theory, thanks to Burkholder-Davis-Gundy's inequality. In the context of rough path theory, however, it does not seem so obvious.


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Additional Information

Yuzuru Inahama
Affiliation: Graduate School of Mathematics, Nagoya University, Furocho, Chikusa-ku, Nagoya 464-8602, Japan
Email: inahama@math.nagoya-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2011-11051-7
Received by editor(s): October 1, 2010
Received by editor(s) in revised form: February 1, 2011
Published electronically: October 11, 2011
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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