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 Electronic Journal of Probability > Vol. 6 (2001) > Paper 17 open journal systems 


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 $int_EAfdmu =0$ for $fin {cal D}(A)$; that is, for each such $mu$, there exists a stationary solution of the martingale problem for A with marginal distribution $ mu$. 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.




Full text: PDF

Pages: 1-52

Published on: January 17, 2001


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Electronic Journal of Probability. ISSN: 1083-6489