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The Annals of Probability 2001, Vol. 29, No. 2, 9791000
 

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

  

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

 

Collections: Engineering