A moment estimate of the derivative process in rough path theory. (English) Zbl 1241.60026
Summary: We prove that the derivative process of a rough differential equation driven by a Brownian rough path has finite \( L^r\)-moment for any \( r \geq 1\). 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.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60G99 | Stochastic processes |
References:
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