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1r G 2002 Kluwer Academic acceptance probability algorithm approximation asset Assumption 2.1 average cost bankruptcy Borel boundary branching processes Changsha Chen consider constant consumption control problem Controlled Markov Chains convergence corresponding cost optimal criterion deﬁned deﬁnition denote deterministic discounted discrete distribution dynamic programming Dynkin ergodic exists Feller ﬁnd ﬁnite ﬁrst ﬁxed given Hence holds implies inequality inﬁnite jump KLSS Lemma linear program Markov chain Markov decision processes Markov processes Markov property Markov skeleton process martingale Math MDP1 measurable function minimal nonnegative obtained optimal policies optimal stationary policy optimal value function optimality equation PDMP policy 1r policy f Proof prove q-matrix Q-process satisﬁes Section sequence Sethi Sierpinski carpet SMDP solution space stationary policy stochastic process strategy strongly connected components subset Suppose Theorem 3.1 tion transition function transition probability u-invariant unique
Continuous-time controlled Markov chains
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