International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 803724, 20 pages
Research Article

General LQG Homing Problems in One Dimension

1Département de Mathématiques et de Génie Industriel, École Polytechnique, C.P.6079, Succursale Centre-ville, Montréal, QC, Canada H3C 3A7
2Département de Mathématiques et de Statistique, Université de Montréal, C.P.6128, Succursale Centre-ville, Montréal, QC, Canada H3C 3J7

Received 26 May 2012; Revised 23 July 2012; Accepted 10 August 2012

Academic Editor: Jiongmin Yong

Copyright © 2012 Mario Lefebvre and Foued Zitouni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Optimal control problems for one-dimensional diffusion processes in the interval ( ) are considered. The aim is either to maximize or to minimize the time spent by the controlled processes in ( ). Exact solutions are obtained when the processes are symmetrical with respect to . Approximate solutions are derived in the asymmetrical case. The one-barrier cases are also treated. Examples are presented.