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)

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10.1002/mana.200810843

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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",

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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

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SN - 0025-584X

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ER -

Large deviations for discontinuous additive functionals of symmetric stable processes

Abstract

Keywords

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