Summary: The Annals of Probability
2006, Vol. 34, No. 5, 1864­1909
DOI: 10.1214/009117906000000359
© Institute of Mathematical Statistics, 2006
SINGULAR CONTROL WITH STATE CONSTRAINTS ON
UNBOUNDED DOMAIN
BY RAMI ATAR1 AND AMARJIT BUDHIRAJA2
Technion­Israel Institute of Technology and University of North Carolina
We study a class of stochastic control problems where a cost of the form
E
[0,)
e-s[ (Xs)ds + h(Y
s )d|Y|s](0.1)
is to be minimized over control processes Y whose increments take values in
a cone Y of Rp, keeping the state process X = x +B +GY in a cone X of Rk,
k p. Here, x X, B is a Brownian motion with drift b and covariance ,
G is a fixed matrix, and Y is the Radon­Nikodym derivative dY/d|Y|. Let
L = -(1/2)trace( D2) - b · D where D denotes the gradient. Solutions to
the corresponding dynamic programming PDE,
[(L + )f - ] sup

Source: Atar, Rami - Department of Electrical Engineering, Technion, Israel Institute of Technology

Collections: Engineering