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Probab. Theory Relat. Fields DOI 10.1007/s00440-007-0104-z

Summary: Probab. Theory Relat. Fields
DOI 10.1007/s00440-007-0104-z
Deterministic and stochastic differential inclusions
with multiple surfaces of discontinuity
Rami Atar Amarjit Budhiraja Kavita Ramanan
Received: 7 December 2006 / Revised: 4 September 2007
Springer-Verlag 2008
Abstract We consider a class of deterministic and stochastic dynamical systems
with discontinuous drift f and solutions that are constrained to live in a given closed
domain G in Rn according to a constraint vector field D() specified on the boundary
G of the domain. Specifically, we consider equations of the form
= + + u, (t) F((t)), a.e. t
for u in an appropriate class of functions, where is the "constraining term" in the
Skorokhod problem specified by (G, D) and F is the set-valued upper semiconti-
nuous envelope of f . The case G = Rn (when there is no constraining mechanism)
and u is absolutely continuous corresponds to the well known setting of differential
R. Atar was partially supported by the Israel Science Foundation (grant 126/02), the NSF (grant
DMS-0600206), and the fund for promotion of research at the Technion.
A. Budhiraja was partially supported by the ARO (grants W911NF-04-1-0230,W911NF-0-1-0080).
K. Ramanan was partially Supported by the NSF (grants DMS-0406191, DMI-0323668-0000000965,


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


Collections: Engineering