Boundary Crossing of Brownian Motion

This is a research report about my work on sequential statistic~ during 1980 - 1984.

Boundary Crossing of Brownian Motion

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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Boundary Crossing of Brownian Motion
Language: en
Pages: 143
Authors: Hans R. Lerche
Categories: Mathematics
Type: BOOK - Published: 2013-11-11 - Publisher: Springer Science & Business Media

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
Boundary Crossing of Brownian Motion
Language: en
Pages: 152
Authors: Hans R. Lerche
Categories: Mathematics
Type: BOOK - Published: 2014-01-15 - Publisher:

Books about Boundary Crossing of Brownian Motion
Brownian Motion and Stochastic Calculus
Language: en
Pages: 470
Authors: Ioannis Karatzas, Steven Shreve
Categories: Mathematics
Type: BOOK - Published: 2014-03-27 - Publisher: Springer

A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this
Working paper
Language: un
Pages:
Authors: Thomas H. Scheike
Categories: Mathematics
Type: BOOK - Published: 1990 - Publisher:

Books about Working paper
Boundary Crossing Probability for Brownian Motion and General Boundaries
Language: en
Pages: 12
Authors: Liqun Wang, Klaus Poetzelberger, University of Southern California. Department of Economics
Categories: Brownian motion processes
Type: BOOK - Published: 1994 - Publisher:

Books about Boundary Crossing Probability for Brownian Motion and General Boundaries