Laplace approximations for large deviations of diffusion processes on Euclidean spaces

Song Liang

doi:10.2969/jmsj/1158242071

Laplace approximations for large deviations of diffusion processes on Euclidean spaces

Song Liang^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

Consider a class of uniformly elliptic diffusion processes (X_t)_{t ≥ 0} on Euclidean spaces R^d. We give an estimate of E^P_x[exp(TΦ(1/T ∫^T₀ δ X_t dt))||X_T = y] as T → ∞ up to the order 1+o(1), where δ, means the delta measure, and Φ is a function on the set of measures on R^d. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.

Original language	English
Pages (from-to)	557-592
Number of pages	36
Journal	Journal of the Mathematical Society of Japan
Volume	57
Issue number	2
DOIs	https://doi.org/10.2969/jmsj/1158242071
Publication status	Published - 2005
Externally published	Yes

Keywords

Diffusion process
Euclidean space
Laplace approximation
Large deviation

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/1158242071

Cite this

@article{e8ec4f390ea146f194456a8ffbe671fe,

title = "Laplace approximations for large deviations of diffusion processes on Euclidean spaces",

abstract = "Consider a class of uniformly elliptic diffusion processes (Xt)t ≥ 0 on Euclidean spaces Rd. We give an estimate of EPx[exp(TΦ(1/T ∫T0 δ Xt dt))||XT = y] as T → ∞ up to the order 1+o(1), where δ, means the delta measure, and Φ is a function on the set of measures on Rd. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.",

keywords = "Diffusion process, Euclidean space, Laplace approximation, Large deviation",

author = "Song Liang",

year = "2005",

doi = "10.2969/jmsj/1158242071",

language = "English",

volume = "57",

pages = "557--592",

journal = "Journal of the Mathematical Society of Japan",

issn = "0025-5645",

publisher = "Mathematical Society of Japan - Kobe University",

number = "2",

}

TY - JOUR

T1 - Laplace approximations for large deviations of diffusion processes on Euclidean spaces

AU - Liang, Song

PY - 2005

Y1 - 2005

N2 - Consider a class of uniformly elliptic diffusion processes (Xt)t ≥ 0 on Euclidean spaces Rd. We give an estimate of EPx[exp(TΦ(1/T ∫T0 δ Xt dt))||XT = y] as T → ∞ up to the order 1+o(1), where δ, means the delta measure, and Φ is a function on the set of measures on Rd. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.

AB - Consider a class of uniformly elliptic diffusion processes (Xt)t ≥ 0 on Euclidean spaces Rd. We give an estimate of EPx[exp(TΦ(1/T ∫T0 δ Xt dt))||XT = y] as T → ∞ up to the order 1+o(1), where δ, means the delta measure, and Φ is a function on the set of measures on Rd. This is a generalization of the works by Bolthausen-Deuschel-Tamura [3] and Kusuoka-Liang [10], which studied the same problems for processes on compact state spaces.

KW - Diffusion process

KW - Euclidean space

KW - Laplace approximation

KW - Large deviation

UR - http://www.scopus.com/inward/record.url?scp=22144470805&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22144470805&partnerID=8YFLogxK

U2 - 10.2969/jmsj/1158242071

DO - 10.2969/jmsj/1158242071

M3 - Article

AN - SCOPUS:22144470805

SN - 0025-5645

VL - 57

SP - 557

EP - 592

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

IS - 2

ER -

Laplace approximations for large deviations of diffusion processes on Euclidean spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this