Boundary Crossing of Brownian Motion
Title | Boundary Crossing of Brownian Motion PDF eBook |
Author | Hans R. Lerche |
Publisher | |
Pages | 152 |
Release | 2014-01-15 |
Genre | |
ISBN | 9781461565703 |
Boundary Crossing of Brownian Motion
Title | Boundary Crossing of Brownian Motion PDF eBook |
Author | Hans R. Lerche |
Publisher | Springer Science & Business Media |
Pages | 147 |
Release | 2013-11-11 |
Genre | Mathematics |
ISBN | 1461565693 |
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.
Working paper
Title | Working paper PDF eBook |
Author | Thomas H. Scheike |
Publisher | |
Pages | |
Release | 1990 |
Genre | |
ISBN |
Boundary Crossing Probability for Brownian Motion and General Boundaries
Title | Boundary Crossing Probability for Brownian Motion and General Boundaries PDF eBook |
Author | Liqun Wang |
Publisher | |
Pages | 12 |
Release | 1994 |
Genre | Brownian motion processes |
ISBN |
A Boundary Crossing Result for the Brownian Motion
Title | A Boundary Crossing Result for the Brownian Motion PDF eBook |
Author | Thomas H. Scheike |
Publisher | |
Pages | 5 |
Release | 1990 |
Genre | |
ISBN |
Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes
Title | Linear and Non-linear Boundary Crossing Probabilities for Brownian Motion and Related Processes PDF eBook |
Author | Tung-Lung Wu (Jr.) |
Publisher | |
Pages | 240 |
Release | 2012 |
Genre | |
ISBN |
We propose a simple and general method to obtain the boundary crossing probability for Brownian motion. This method can be easily extended to higher dimensional of Brownian motion. It also covers certain classes of stochastic processes associated with Brownian motion. The basic idea of the method is based on being able to construct a nite Markov chain such that the boundary crossing probability of Brownian motion is obtained as the limiting probability of the nite Markov chain entering a set of absorbing states induced by the boundary. Numerical results are given to illustrate our method.
Asymptotic Problems Related to Boundary Crossing of One-dimensional Shifted Brownian Motion
Title | Asymptotic Problems Related to Boundary Crossing of One-dimensional Shifted Brownian Motion PDF eBook |
Author | Moshe Pollak |
Publisher | |
Pages | 92 |
Release | 1973 |
Genre | Asymptotic expansions |
ISBN |