Adjoint Processes
Notes on controlled markov processes
Check out "DISCRETE-TIME CONTROLLED MARKOV PROCESSES WITH AVERAGE COST CRITERION: A SURVEY" http://users.ece.utexas.edu/~ari/
See also same page for notes on controllability of linear systems "the adjoint of a linear map".
See also Haussman "On the Adjoint Process for Optimal Control of Diffusion Processes"
media:Haussman_Adjoint_Optimal_Control.pdf and media:Haussman_Adjoint_Optimal_Control_Errata.pdf
and Borwein, "Adjoint Process Duality" http://www.jstor.org/pss/3689309