A Moment estimate of the derivative process in rough path theory

Yuzuru Inahama

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

A Moment estimate of the derivative process in rough path theory

Yuzuru Inahama

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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
Pages (from-to)	2183-2191
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	140
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2011-11051-7
Publication status	Published - 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2011-11051-7

Cite this

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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.

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

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

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A Moment estimate of the derivative process in rough path theory

Abstract

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