Large deviations for discontinuous additive functionals of symmetric stable processes

Masayoshi Takeda; Kaneharu Tsuchida

doi:10.1002/mana.200810843

Large deviations for discontinuous additive functionals of symmetric stable processes

Masayoshi Takeda, Kaneharu Tsuchida

SCI - Mathematics

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

1 Citation (Scopus)

Abstract

Let X_t be a symmetric stable process on d-dimensional Euclidean space R^d Let F(x, y) be a symmetric positive bounded function on R^d x R^d vanishing on the diagonal set and define a discontinuous additive functional by A_t(F) = σ_{0 < s ≤ t}F(X_s-, X_s). We establish the large deviation principle of A_t(F)/t by employing the Gärtner-Ellis theorem.

Original language	English
Pages (from-to)	1148-1171
Number of pages	24
Journal	Mathematische Nachrichten
Volume	284
Issue number	8-9
DOIs	https://doi.org/10.1002/mana.200810843
Publication status	Published - 2011 Jun

Keywords

Discontinuous additive functional
Gärtner-Ellis theorem
Large deviation
Symmetric stable process

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1002/mana.200810843

Fingerprint Dive into the research topics of 'Large deviations for discontinuous additive functionals of symmetric stable processes'. Together they form a unique fingerprint.

Cite this

@article{b6762416a7d446c9a9ae4961f62a5eac,

title = "Large deviations for discontinuous additive functionals of symmetric stable processes",

abstract = "Let Xt be a symmetric stable process on d-dimensional Euclidean space Rd Let F(x, y) be a symmetric positive bounded function on Rd x Rd vanishing on the diagonal set and define a discontinuous additive functional by At(F) = σ0 < s ≤ tF(Xs-, Xs). We establish the large deviation principle of At(F)/t by employing the G{\"a}rtner-Ellis theorem.",

keywords = "Discontinuous additive functional, G{\"a}rtner-Ellis theorem, Large deviation, Symmetric stable process",

author = "Masayoshi Takeda and Kaneharu Tsuchida",

year = "2011",

month = jun,

doi = "10.1002/mana.200810843",

language = "English",

volume = "284",

pages = "1148--1171",

journal = "Mathematische Nachrichten",

issn = "0025-584X",

publisher = "Wiley-VCH Verlag",

number = "8-9",

}

TY - JOUR

T1 - Large deviations for discontinuous additive functionals of symmetric stable processes

AU - Takeda, Masayoshi

AU - Tsuchida, Kaneharu

PY - 2011/6

Y1 - 2011/6

N2 - Let Xt be a symmetric stable process on d-dimensional Euclidean space Rd Let F(x, y) be a symmetric positive bounded function on Rd x Rd vanishing on the diagonal set and define a discontinuous additive functional by At(F) = σ0 < s ≤ tF(Xs-, Xs). We establish the large deviation principle of At(F)/t by employing the Gärtner-Ellis theorem.

AB - Let Xt be a symmetric stable process on d-dimensional Euclidean space Rd Let F(x, y) be a symmetric positive bounded function on Rd x Rd vanishing on the diagonal set and define a discontinuous additive functional by At(F) = σ0 < s ≤ tF(Xs-, Xs). We establish the large deviation principle of At(F)/t by employing the Gärtner-Ellis theorem.

KW - Discontinuous additive functional

KW - Gärtner-Ellis theorem

KW - Large deviation

KW - Symmetric stable process

UR - http://www.scopus.com/inward/record.url?scp=79956307163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956307163&partnerID=8YFLogxK

U2 - 10.1002/mana.200810843

DO - 10.1002/mana.200810843

M3 - Article

AN - SCOPUS:79956307163

VL - 284

SP - 1148

EP - 1171

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 8-9

ER -