On the monotonicity of a function related to the local time of a symmetric Lévy process

Renming Song; Zoran Vondraček

doi:10.1016/j.spl.2006.03.013

On the monotonicity of a function related to the local time of a symmetric Lévy process

Renming Song, Zoran Vondraček

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

Abstract

Let ψ be the characteristic exponent of a symmetric Lévy process X. The functionh (x) = frac(2, π) ∫₀^∞ frac(1 - cos (λ x), ψ (λ)) d λappears in various studies on the local time of X. We study monotonicity properties of the function h. In case when X is a subordinate Brownian motion, we show that x {mapping} h (sqrt(x)) is a Bernstein function.

Original language	English (US)
Pages (from-to)	1522-1528
Number of pages	7
Journal	Statistics and Probability Letters
Volume	76
Issue number	14
DOIs	https://doi.org/10.1016/j.spl.2006.03.013
State	Published - Aug 1 2006

Keywords

Bernstein function
Local time
Lévy processes
Subordinate Brownian motion

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Online availability

10.1016/j.spl.2006.03.013

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abstract = "Let ψ be the characteristic exponent of a symmetric L{\'e}vy process X. The functionh (x) = frac(2, π) ∫0∞ frac(1 - cos (λ x), ψ (λ)) d λappears in various studies on the local time of X. We study monotonicity properties of the function h. In case when X is a subordinate Brownian motion, we show that x {mapping} h (sqrt(x)) is a Bernstein function.",

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N2 - Let ψ be the characteristic exponent of a symmetric Lévy process X. The functionh (x) = frac(2, π) ∫0∞ frac(1 - cos (λ x), ψ (λ)) d λappears in various studies on the local time of X. We study monotonicity properties of the function h. In case when X is a subordinate Brownian motion, we show that x {mapping} h (sqrt(x)) is a Bernstein function.

AB - Let ψ be the characteristic exponent of a symmetric Lévy process X. The functionh (x) = frac(2, π) ∫0∞ frac(1 - cos (λ x), ψ (λ)) d λappears in various studies on the local time of X. We study monotonicity properties of the function h. In case when X is a subordinate Brownian motion, we show that x {mapping} h (sqrt(x)) is a Bernstein function.

KW - Bernstein function

KW - Local time

KW - Lévy processes

KW - Subordinate Brownian motion

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On the monotonicity of a function related to the local time of a symmetric Lévy process

Abstract

Keywords

ASJC Scopus subject areas

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