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Boundary Crossing Of Brownian Motion


Boundary Crossing Of Brownian Motion
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Boundary Crossing Of Brownian Motion


Boundary Crossing Of Brownian Motion
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Author : Hans R. Lerche
language : en
Publisher:
Release Date : 2014-01-15

Boundary Crossing Of Brownian Motion written by Hans R. Lerche and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.




Boundary Crossing Of Brownian Motion


Boundary Crossing Of Brownian Motion
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Author : Hans R. Lerche
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Boundary Crossing Of Brownian Motion written by Hans R. Lerche and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.


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


Working Paper
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Author : Thomas H. Scheike
language : un
Publisher:
Release Date : 1990

Working Paper written by Thomas H. Scheike and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.




Boundary Crossing Probability For Brownian Motion And General Boundaries


Boundary Crossing Probability For Brownian Motion And General Boundaries
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Author : Liqun Wang
language : en
Publisher:
Release Date : 1994

Boundary Crossing Probability For Brownian Motion And General Boundaries written by Liqun Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Brownian motion processes categories.




Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes


Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes
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Author : Tung-Lung Wu (Jr.)
language : en
Publisher:
Release Date : 2012

Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes written by Tung-Lung Wu (Jr.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.


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.



A Boundary Crossing Result For The Brownian Motion


A Boundary Crossing Result For The Brownian Motion
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Author : Thomas H. Scheike
language : en
Publisher:
Release Date : 1990

A Boundary Crossing Result For The Brownian Motion written by Thomas H. Scheike and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.




Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes


Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes
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Author : Tung-Lung Jr Wu
language : en
Publisher:
Release Date : 2010

Linear And Non Linear Boundary Crossing Probabilities For Brownian Motion And Related Processes written by Tung-Lung Jr Wu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.


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


Asymptotic Problems Related To Boundary Crossing Of One Dimensional Shifted Brownian Motion
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Author : Moshe Pollak
language : en
Publisher:
Release Date : 1973

Asymptotic Problems Related To Boundary Crossing Of One Dimensional Shifted Brownian Motion written by Moshe Pollak and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Asymptotic expansions categories.




Brownian Motion And Stochastic Calculus


Brownian Motion And Stochastic Calculus
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Author : Ioannis Karatzas
language : en
Publisher: Springer
Release Date : 2014-03-27

Brownian Motion And Stochastic Calculus written by Ioannis Karatzas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-27 with Mathematics categories.


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 context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.



A New Approach To The Computation Of First Passage Time Distribution For Brownian Motion


A New Approach To The Computation Of First Passage Time Distribution For Brownian Motion
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Author : Zhiyong Jin
language : en
Publisher:
Release Date : 2014

A New Approach To The Computation Of First Passage Time Distribution For Brownian Motion written by Zhiyong Jin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.


This thesis consists of two novel contributions to the computation of first passage time distribution for Brownian motion. First, we extend the known formula for boundary crossing probabilities for Brownian motion to the discontinuous piecewise linear boundary. Second, we derive explicit formula for the first passage time density of Brownian motion crossing piecewise linear boundary. Further, we demonstrate how to approximate the boundary crossing probabilities and density for general nonlinear boundaries. Moreover, we use Monte Carlo simulation method and develop algorithms for the numerical computation. This method allows one to assess the accuracy of the numerical approximation. Our approach can be further extended to compute two-sided boundary crossing probabilities.