Title :
The value and location of the maximum of brownian motion
Author_Institution :
Australian Defense Scientific Service, Melbourne, Australia
fDate :
10/1/1968 12:00:00 AM
Abstract :
A derivation is given, using the reflection principle, of the distribution of the value and location of the maximum on an interval of Brownian motion with known end-point values. The density of the location is infinite at the end point of greater value and decreases monotonically to zero at the other. A procedure is briefly discussed for using the distribution in a pointwise sequential search for the location of the maximum.
Keywords :
Optimization methods; Contracts; Covariance matrix; Eigenvalues and eigenfunctions; Equations; Gaussian noise; Maximum likelihood estimation; Monte Carlo methods; Random variables; Transfer functions; Vectors;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.1968.1098976
