 
Summary: The Annals of Probability
2001, Vol. 29, No. 2, 9791000
ON POSITIVE RECURRENCE OF CONSTRAINED
DIFFUSION PROCESSES
By Rami Atar, Amarjit Budhiraja1
and Paul Dupuis2
TechnionIsrael Institute of Technology, University of North Carolina, Chapel
Hill and Brown University
Let G k be a convex polyhedral cone with vertex at the origin
given as the intersection of half spaces Gi i = 1 N , where ni and
di denote the inward normal and direction of constraint associated with
Gi, respectively. Stability properties of a class of diffusion processes, con
strained to take values in G, are studied under the assumption that the
Skorokhod problem defined by the data ni di i = 1 N is well
posed and the Skorokhod map is Lipschitz continuous. Explicit conditions
on the drift coefficient, b · , of the diffusion process are given under which
the constrained process is positive recurrent and has a unique invariant
measure. Define
= 
N
