TY - JOUR
T1 - Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis
AU - Arapostathis, Ari
AU - Pang, Guodong
AU - Zheng, Yi
N1 - Funding Information:
This research was supported in part by the Army Research Office through grant W911NF-17-1-001 , and in part by the National Science Foundation through grants DMS-1715210 , CMMI-1635410 and DMS-1715875 , and in part by Office of Naval Research through grant N00014-16-1-2956 and was approved for public release under DCN #43-5439-19.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2020/11
Y1 - 2020/11
N2 - We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of Arapostathis et al. (2019) to running costs that are not near-monotone. This generality is needed in applications such as optimal scheduling of large-scale parallel server networks. We provide a full characterizations of optimality via the Hamilton–Jacobi–Bellman (HJB) equation, for which we additionally exhibit regularity of solutions under mild hypotheses. In addition, we show that optimal stationary Markov controls are a.s. pathwise optimal. Lastly, we show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. This is useful for constructing asymptotically optimal scheduling policies for multiclass parallel server networks.
AB - We study the ergodic control problem for a class of controlled jump diffusions driven by a compound Poisson process. This extends the results of Arapostathis et al. (2019) to running costs that are not near-monotone. This generality is needed in applications such as optimal scheduling of large-scale parallel server networks. We provide a full characterizations of optimality via the Hamilton–Jacobi–Bellman (HJB) equation, for which we additionally exhibit regularity of solutions under mild hypotheses. In addition, we show that optimal stationary Markov controls are a.s. pathwise optimal. Lastly, we show that one can fix a stable control outside a compact set and obtain near-optimal solutions by solving the HJB on a sufficiently large bounded domain. This is useful for constructing asymptotically optimal scheduling policies for multiclass parallel server networks.
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U2 - 10.1016/j.spa.2020.06.008
DO - 10.1016/j.spa.2020.06.008
M3 - Article
AN - SCOPUS:85087011815
VL - 130
SP - 6733
EP - 6756
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 11
ER -