Stationary Solutions and Forward Equations for Controlled and Singular Martingale Problems
Thomas G. Kurtz, University of Wisconsin, Madison
Richard H. Stockbridge, University of Kentucky
Abstract
Stationary distributions of Markov
processes can typically be characterized as probability measures that
annihilate the generator in the sense that
for
;
that is, for each such
,
there exists a stationary solution of the martingale problem for
A
with marginal distribution
.
This result is extended to models corresponding to
martingale problems that include
absolutely continuous and singular (with respect to time) components and
controls. Analogous results for the forward equation follow as a corollary.
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