A moment estimate of the derivative process in rough path theory

Inahama, Yuzuru

doi:10.1090/S0002-9939-2011-11051-7

A moment estimate of the derivative process in rough path theory
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Proc. Amer. Math. Soc. 140 (2012), 2183-2191 Request permission

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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