Ergodic control of diffusions with compound Poisson jumps under a general structural hypothesis

Ari Arapostathis, Guodong Pang, Yi Zheng

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)6733-6756
Number of pages24
JournalStochastic Processes and their Applications
Volume130
Issue number11
DOIs
StatePublished - Nov 2020

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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