On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control

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dc.creatorKaise, Hidehiro
dc.creatorSheu, Shuenn-Jyi
dc.date2006-02-27
dc.date.accessioned2026-07-07T07:03:51Z
dc.date.available2026-07-07T07:03:51Z
dc.descriptionBellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that the nonlinear term is positive quadratic form on first-order partial derivatives of solution, which includes linear exponential quadratic Gaussian control problem. In this paper we prove that the equation in general has multiple solutions. We shall specify the set of all the classical solutions and classify the solutions by a global behavior of the diffusion process associated with the given solution. The solution associated with ergodic diffusion process plays particular role. We shall also prove the uniqueness of such solution. Furthermore, the solution which gives us ergodicity is stable under perturbation of coefficients. Finally, we have a representation result for the solution corresponding to the ergodic diffusion.
dc.descriptionPublished at http://dx.doi.org/10.1214/009117905000000431 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0602625
dc.identifierhttp://arxiv.org/abs/math/0602625
dc.identifierAnnals of Probability 2006, Vol. 34, No. 1, 284-320
dc.identifierdoi:10.1214/009117905000000431
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/109133
dc.subjectProbability
dc.subject60G35 (Primary) 60H30, 93E20 (Secondary)
dc.titleOn the structure of solutions of ergodic type Bellman equation related to risk-sensitive control
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