期刊
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
卷 57, 期 2, 页码 1516-1540出版社
SIAM PUBLICATIONS
DOI: 10.1137/18M1166717
关键词
controlled jump diffusions; compound Poisson process; Levy process; ergodic control; Hamilton-Jacobi-Bellman equation
资金
- National Science Foundation [DMS-1540162, DMS-1715210, CMMI-1538149, DMS-1715875]
- Army Research Office [W911NF-17-1-0019]
- Office of Naval Research [N00014-16-1-2956]
We study the ergodic control problem for a class of jump diffusions in R-d which are controlled through the drift with bounded controls. The Levy measure is finite, but has no particular structure; it can be anisotropic and singular. Moreover, there is no blanket ergodicity assumption for the controlled process. Unstable behavior is discouraged by the running cost which satisfies a mild coercive hypothesis (i.e., is near-monotone). We first study the problem in its weak formulation as an optimization problem on the space of infinitesimal ergodic occupation measures and derive the Hamilton-Jacobi-Bellman equation under minimal assumptions on the parameters, including verification of optimality results, using only analytical arguments. We also examine the regularity of invariant measures. Then, we address the jump diffusion model and obtain a complete characterization of optimality.
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