Asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths

Yuzuru Inahama, Hiroshi Kawabi

研究成果: Article

15 引用 (Scopus)

抄録

In this paper, we establish asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths under the condition that the phase function has finitely many non-degenerate minima. Our main tool is the Banach space-valued rough path theory of T. Lyons. We use a large deviation principle and the stochastic Taylor expansion with respect to the topology of the space of geometric rough paths. This is a continuation of a series of papers by Inahama [Y. Inahama, Laplace's method for the laws of heat processes on loop spaces, J. Funct. Anal. 232 (2006) 148-194] and by Inahama and Kawabi [Y. Inahama, H. Kawabi, Large deviations for heat kernel measures on loop spaces via rough paths, J. London Math. Soc. 73 (3) (2006) 797-816], [Y. Inahama, H. Kawabi, On asymptotics of certain Banach space-valued Itô functionals of Brownian rough paths, in: Proceedings of the Abel Symposium 2005, Stochastic Analysis and Applications, A Symposium in Honor of Kiyosi Itô, Springer, Berlin, in press. Available at: http://www.abelprisen.no/no/abelprisen/deltagere_2005.html].

元の言語English
ページ(範囲)270-322
ページ数53
ジャーナルJournal of Functional Analysis
243
発行部数1
DOI
出版物ステータスPublished - 2007 2 1
外部発表Yes

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Rough Paths
Laplace Approximation
Asymptotic Expansion
Loop Space
Banach space
Laplace's Method
Large Deviation Principle
Stochastic Analysis
Taylor Expansion
Heat Kernel
Large Deviations
Continuation
Heat
Topology
Series

ASJC Scopus subject areas

  • Analysis

これを引用

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AB - In this paper, we establish asymptotic expansions for the Laplace approximations for Itô functionals of Brownian rough paths under the condition that the phase function has finitely many non-degenerate minima. Our main tool is the Banach space-valued rough path theory of T. Lyons. We use a large deviation principle and the stochastic Taylor expansion with respect to the topology of the space of geometric rough paths. This is a continuation of a series of papers by Inahama [Y. Inahama, Laplace's method for the laws of heat processes on loop spaces, J. Funct. Anal. 232 (2006) 148-194] and by Inahama and Kawabi [Y. Inahama, H. Kawabi, Large deviations for heat kernel measures on loop spaces via rough paths, J. London Math. Soc. 73 (3) (2006) 797-816], [Y. Inahama, H. Kawabi, On asymptotics of certain Banach space-valued Itô functionals of Brownian rough paths, in: Proceedings of the Abel Symposium 2005, Stochastic Analysis and Applications, A Symposium in Honor of Kiyosi Itô, Springer, Berlin, in press. Available at: http://www.abelprisen.no/no/abelprisen/deltagere_2005.html].

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