### 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 ≥ 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.

Original language | English |
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Pages (from-to) | 2183-2191 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 6 |

DOIs | |

Publication status | Published - Feb 27 2012 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

**A Moment estimate of the derivative process in rough path theory.** / Inahama, Yuzuru.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 140, no. 6, pp. 2183-2191. https://doi.org/10.1090/S0002-9939-2011-11051-7

}

TY - JOUR

T1 - A Moment estimate of the derivative process in rough path theory

AU - Inahama, Yuzuru

PY - 2012/2/27

Y1 - 2012/2/27

N2 - 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 ≥ 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.

AB - 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 ≥ 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.

UR - http://www.scopus.com/inward/record.url?scp=84857250805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857250805&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-2011-11051-7

DO - 10.1090/S0002-9939-2011-11051-7

M3 - Article

AN - SCOPUS:84857250805

VL - 140

SP - 2183

EP - 2191

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -