Lower functions for processes with stationary independent increments

In Suk Wee

doi:10.1007/BF00959617

Lower functions for processes with stationary independent increments

In Suk Wee

* Honorary professors

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10 Citations (Scopus)

Abstract

Let {X_t} be a R¹-valued process with stationary independent increments and {Mathematical expression}. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing function h(t) such that lim inf A_t/h(t)=C a.s. as t→0 and t→∞, for some positive finite constant C when h(t) takes a particular form. Also two analytic conditions are considered as application.

Original language	English
Pages (from-to)	551-566
Number of pages	16
Journal	Probability Theory and Related Fields
Volume	77
Issue number	4
DOIs	https://doi.org/10.1007/BF00959617
Publication status	Published - 1988 Dec

ASJC Scopus subject areas

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF00959617

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title = "Lower functions for processes with stationary independent increments",

abstract = "Let {Xt} be a R1-valued process with stationary independent increments and {Mathematical expression}. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing function h(t) such that lim inf At/h(t)=C a.s. as t→0 and t→∞, for some positive finite constant C when h(t) takes a particular form. Also two analytic conditions are considered as application.",

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T1 - Lower functions for processes with stationary independent increments

AU - Wee, In Suk

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N2 - Let {Xt} be a R1-valued process with stationary independent increments and {Mathematical expression}. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing function h(t) such that lim inf At/h(t)=C a.s. as t→0 and t→∞, for some positive finite constant C when h(t) takes a particular form. Also two analytic conditions are considered as application.

AB - Let {Xt} be a R1-valued process with stationary independent increments and {Mathematical expression}. In this paper we find a sufficient condition for there to exist nonnegative and nondecreasing function h(t) such that lim inf At/h(t)=C a.s. as t→0 and t→∞, for some positive finite constant C when h(t) takes a particular form. Also two analytic conditions are considered as application.

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U2 - 10.1007/BF00959617

DO - 10.1007/BF00959617

M3 - Article

AN - SCOPUS:0039876338

SN - 0178-8051

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SP - 551

EP - 566

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 4

ER -

Lower functions for processes with stationary independent increments

Abstract

ASJC Scopus subject areas

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