Translator Disclaimer
August, 1984 Trivariate Density of Brownian Motion, Its Local and Occupation Times, with Application to Stochastic Control
Ioannis Karatzas, Steven E. Shreve
Ann. Probab. 12(3): 819-828 (August, 1984). DOI: 10.1214/aop/1176993230

Abstract

We compute the joint density of Brownian motion, its local time at the origin, and its occupation time of $\lbrack 0, \infty)$. Two derivations of the main result are offered; one is computational, whereas the other uses some of the deep properties of Brownian local time. We use the result to compute the transition probabilities of the optimal process in a stochastic control problem.

Citation

Download Citation

Ioannis Karatzas. Steven E. Shreve. "Trivariate Density of Brownian Motion, Its Local and Occupation Times, with Application to Stochastic Control." Ann. Probab. 12 (3) 819 - 828, August, 1984. https://doi.org/10.1214/aop/1176993230

Information

Published: August, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0544.60069
MathSciNet: MR744236
Digital Object Identifier: 10.1214/aop/1176993230

Subjects:
Primary: 60J65
Secondary: 60G17, 93E20

Rights: Copyright © 1984 Institute of Mathematical Statistics

JOURNAL ARTICLE
10 PAGES


SHARE
Vol.12 • No. 3 • August, 1984
Back to Top