Laws of the iterated logarithm for symmetric stable processes

Philip S. Griffin

doi:10.1007/BF00532641

Laws of the iterated logarithm for symmetric stable processes

Philip S. Griffin

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

11 Scopus citations

Abstract

Let X(t) be a symmetric stable process of index α> 1 with local time L(t, x) and define R(t)=|{x:X(s)=x for some s≦t}| and L^*(t) = sup{L(t, x): x∈ℝ¹}. We prove that {Mathematical expression} where c₁, c₂∈(0, ∞). A law of the iterated logarithm is also given for X(t) when its large jumps are excluded.

Original language	English (US)
Pages (from-to)	271-285
Number of pages	15
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	68
Issue number	3
DOIs	https://doi.org/10.1007/BF00532641
State	Published - Sep 1985
Externally published	Yes

ASJC Scopus subject areas

Analysis
Statistics and Probability
General Mathematics

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10.1007/BF00532641

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abstract = "Let X(t) be a symmetric stable process of index α> 1 with local time L(t, x) and define R(t)=|{x:X(s)=x for some s≦t}| and L*(t) = sup{L(t, x): x∈ℝ1}. We prove that {Mathematical expression} where c1, c2∈(0, ∞). A law of the iterated logarithm is also given for X(t) when its large jumps are excluded.",

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N2 - Let X(t) be a symmetric stable process of index α> 1 with local time L(t, x) and define R(t)=|{x:X(s)=x for some s≦t}| and L*(t) = sup{L(t, x): x∈ℝ1}. We prove that {Mathematical expression} where c1, c2∈(0, ∞). A law of the iterated logarithm is also given for X(t) when its large jumps are excluded.

AB - Let X(t) be a symmetric stable process of index α> 1 with local time L(t, x) and define R(t)=|{x:X(s)=x for some s≦t}| and L*(t) = sup{L(t, x): x∈ℝ1}. We prove that {Mathematical expression} where c1, c2∈(0, ∞). A law of the iterated logarithm is also given for X(t) when its large jumps are excluded.

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Laws of the iterated logarithm for symmetric stable processes

Abstract

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