# Sample path average optimality of Markov control processes with strictly unbounded cost

Applicationes Mathematicae (1999)

- Volume: 26, Issue: 4, page 363-381
- ISSN: 1233-7234

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topVega-Amaya, Oscar. "Sample path average optimality of Markov control processes with strictly unbounded cost." Applicationes Mathematicae 26.4 (1999): 363-381. <http://eudml.org/doc/219246>.

@article{Vega1999,

abstract = {We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we show that if such a policy induces a positive Harris recurrent Markov chain, then it is also sample path average (SPAC-) optimal. We apply our results to inventory systems and, in a particular case, we compute explicitly a deterministic stationary SPAC-optimal policy.},

author = {Vega-Amaya, Oscar},

journal = {Applicationes Mathematicae},

keywords = {strictly unbounded costs; sample path average cost criterion; inventory systems; Markov control processes},

language = {eng},

number = {4},

pages = {363-381},

title = {Sample path average optimality of Markov control processes with strictly unbounded cost},

url = {http://eudml.org/doc/219246},

volume = {26},

year = {1999},

}

TY - JOUR

AU - Vega-Amaya, Oscar

TI - Sample path average optimality of Markov control processes with strictly unbounded cost

JO - Applicationes Mathematicae

PY - 1999

VL - 26

IS - 4

SP - 363

EP - 381

AB - We study the existence of sample path average cost (SPAC-) optimal policies for Markov control processes on Borel spaces with strictly unbounded costs, i.e., costs that grow without bound on the complement of compact subsets. Assuming only that the cost function is lower semicontinuous and that the transition law is weakly continuous, we show the existence of a relaxed policy with 'minimal' expected average cost and that the optimal average cost is the limit of discounted programs. Moreover, we show that if such a policy induces a positive Harris recurrent Markov chain, then it is also sample path average (SPAC-) optimal. We apply our results to inventory systems and, in a particular case, we compute explicitly a deterministic stationary SPAC-optimal policy.

LA - eng

KW - strictly unbounded costs; sample path average cost criterion; inventory systems; Markov control processes

UR - http://eudml.org/doc/219246

ER -

## References

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