Marginal Densities of the Least Concave Majorant of Brownian Motion
Carolan, Chris ; Dykstra, Richard
Ann. Statist., Tome 29 (2001) no. 2, p. 1732-1750 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
A clean, closed form, joint density is derived for Brownian motion, its least concave majorant, and its derivative, all at the same fixed point. Some remarkable conditional and marginal distributions follow from this joint density. For example, it is shown that the height of the least concave majorant of Brownian motion at a fixed time point has the same distribution as the distance from the Brownian motion path to its least concave majorant at the same fixed time point. Also, it is shown that conditional on the height of the least concave majorant of Brownian motion at a fixed time point, the left-hand slope of the least concave majorant of Brownian motion at the same fixed time point is uniformly distributed.
Publié le : 2001-12-14
Classification:  Brownian motion,  least concave majorant,  stochastic ordering,  likelihood ratio ordering,  62E15,  62H10 
@article{1015345960,
     author = {Carolan, Chris and Dykstra, Richard},
     title = {Marginal Densities of the Least Concave Majorant of Brownian
			 Motion},
     journal = {Ann. Statist.},
     volume = {29},
     number = {2},
     year = {2001},
     pages = { 1732-1750},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1015345960}
}

Carolan, Chris; Dykstra, Richard. Marginal Densities of the Least Concave Majorant of Brownian
			 Motion. Ann. Statist., Tome 29 (2001) no. 2, pp.  1732-1750. http://gdmltest.u-ga.fr/item/1015345960/