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On coupled systems of Kolmogorov equations with applications to stochastic differential games
We prove that a family of linear bounded evolution operators can be associated, in the space of vector-valued
bounded and continuous functions, to a class of systems of elliptic operators
with unbounded coefficients defined in I\times \Rd (where
is a right-halfline or ) all having the same principal part. We
establish some continuity and representation properties of and a sufficient condition for the evolution operator to be
compact in C_b(\Rd;\R^m). We prove also a uniform weighted gradient estimate
and some of its more relevant consequence
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