The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component

Boris Buchmann; Ross Maller

doi:10.1007/s00440-009-0255-1

The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component

Boris Buchmann^*, Ross Maller

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

We give a "small time" functional version of Chung's "other" law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.

Original language	English
Pages (from-to)	303-330
Number of pages	28
Journal	Probability Theory and Related Fields
Volume	149
Issue number	1
DOIs	https://doi.org/10.1007/s00440-009-0255-1
Publication status	Published - Mar 2011

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AU - Maller, Ross

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N2 - We give a "small time" functional version of Chung's "other" law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.

AB - We give a "small time" functional version of Chung's "other" law of the iterated logarithm for Lévy processes with non-vanishing Brownian component. This is an analogue of the "other" law of the iterated logarithm at "large times" for Lévy processes and random walks with finite variance, as extended to a functional version by Wichura. As one of many possible applications, we mention a functional law for a two-sided passage time process.

KW - Almost sure convergence

KW - Cluster sets

KW - Functional limit theorem

KW - Iterated logarithm laws

KW - Local behaviour

KW - Lévy process

KW - Other law of the iterated logarithm

UR - https://www.scopus.com/pages/publications/79952006766

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DO - 10.1007/s00440-009-0255-1

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VL - 149

SP - 303

EP - 330

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

The small-time Chung-Wichura law for Lévy processes with non-vanishing Brownian component

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