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Schweitzer, Paul J.

On the solvability of Bellman’s functional equations for Markov renewal programming. (English) Zbl 0526.90094

J. Math. Anal. Appl. 96, 13-23 (1983).
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Cited in 5 Documents

MSC:

90C40 Markov and semi-Markov decision processes

Keywords:

Bellman’s functional equations; undiscounted, stationary, infinite horizon Markov renewal programming; finite state and action spaces; maximal gain rate vector; fixed-point equation
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\textit{P. J. Schweitzer}, J. Math. Anal. Appl. 96, 13--23 (1983; Zbl 0526.90094)
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References:

[1] Blackwell, D, Discrete dynamic programming, Ann. of math. statist., 33, 719-726, (1962) · Zbl 0133.12906
[2] Doob, J, Stochastic processes, (1953), Wiley New York
[3] Federgruen, A; Schweitzer, P.J; Federgruen, A; Schweitzer, P.J, A fixed point approach to undiscounted Markov renewal programs, Columbia university, graduate school of business, working paper no. 351A, University of rochester, graduate school of management, working paper no. 8024, (1980), (Revised 1981.) SIAM J. Control, to appear · Zbl 0388.90083
[4] Jewell, W.S, Markov renewal programming, Oper. res., 11, 938-971, (1963) · Zbl 0126.15905
[5] Ortega, J.M; Rheinboldt, W.C, Iterative solution of nonlinear equations in several variables, (1970), Academic Press New York · Zbl 0241.65046
[6] Romanovsky, I.V, On the solvability of Bellman’s functional equation for a Markovian decision process, J. math. anal. appl., 42, 485-498, (1973) · Zbl 0263.90041
[7] Schweitzer, P.J; Federgruen, A, The functional equations of undiscounted Markov renewal programming, Math. oper. res., 3, 308-322, (1978) · Zbl 0388.90083
[8] Schweitzer, P.J, A non-expansive mapping approach to undiscounted semi-Markovian decision processes, University of rochester, graduate school of management, working paper no. 8109, (February 1981)
[9] White, D.J, Dynamic programming, Markov chains, and the method of successive approximations, J. math. anal. appl., 6, 373-376, (1963) · Zbl 0124.36404
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.