Strassen-type functional laws for strong topologies

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Strassen-type functional laws for strong topologies. / Deheuvels, Paul; Lifshits, Mikhail A.

In: Probability Theory and Related Fields, Vol. 97, No. 1-2, 01.03.1993, p. 151-167.

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

Author

Deheuvels, Paul ; Lifshits, Mikhail A. / Strassen-type functional laws for strong topologies. In: Probability Theory and Related Fields. 1993 ; Vol. 97, No. 1-2. pp. 151-167.

BibTeX

@article{cef9e7f9a1dd46a1b733df4980bf4555,

title = "Strassen-type functional laws for strong topologies",

abstract = " Let W(·) denote a Wiener process. The functional law of the iterated logarithm due to Strassen (1964) establishes that the sequence {(2nLLn) -1/2 W(ns)} of functions of s∈[0,1] is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. In this paper, we obtain a general characterization of the topologies under which this statement remains valid.",

keywords = "Mathematics Subject Classifications (1980): 60F17, 60F15, 60F10, 60G15",

author = "Paul Deheuvels and Lifshits, {Mikhail A.}",

year = "1993",

month = mar,

day = "1",

doi = "10.1007/BF01199317",

language = "English",

volume = "97",

pages = "151--167",

journal = "Probability Theory and Related Fields",

issn = "0178-8051",

publisher = "Springer Nature",

number = "1-2",

}

RIS

TY - JOUR

T1 - Strassen-type functional laws for strong topologies

AU - Deheuvels, Paul

AU - Lifshits, Mikhail A.

PY - 1993/3/1

Y1 - 1993/3/1

N2 - Let W(·) denote a Wiener process. The functional law of the iterated logarithm due to Strassen (1964) establishes that the sequence {(2nLLn) -1/2 W(ns)} of functions of s∈[0,1] is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. In this paper, we obtain a general characterization of the topologies under which this statement remains valid.

AB - Let W(·) denote a Wiener process. The functional law of the iterated logarithm due to Strassen (1964) establishes that the sequence {(2nLLn) -1/2 W(ns)} of functions of s∈[0,1] is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. In this paper, we obtain a general characterization of the topologies under which this statement remains valid.

KW - Mathematics Subject Classifications (1980): 60F17, 60F15, 60F10, 60G15

UR - http://www.scopus.com/inward/record.url?scp=21344476517&partnerID=8YFLogxK

U2 - 10.1007/BF01199317

DO - 10.1007/BF01199317

M3 - Article

AN - SCOPUS:21344476517

VL - 97

SP - 151

EP - 167

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 1-2

ER -

ID: 43811941