Lecture Notes in Statistics

Boundary Crossing of Brownian Motion

Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis

Authors: Lerche, Hans R.

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About this book

This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser­ ved in practice.

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Buy this book

eBook $69.99 net
( price for USA )
  • ISBN 978-1-4615-6569-7
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $99.00 net
( price for USA )
  • ISBN 978-0-387-96433-1
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
Boundary Crossing of Brownian Motion
Book Subtitle
Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis
Series Title
Lecture Notes in Statistics
Series Volume
40
Copyright
1986
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-1-4615-6569-7
DOI
10.1007/978-1-4615-6569-7
Softcover ISBN
978-0-387-96433-1
Series ISSN
0930-0325
Edition Number
1
Topics