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Controlled stochastic hybrid processes with discounted cost

Ghosh, Mrinal K and Bagchi, Arunabha (2004) Controlled stochastic hybrid processes with discounted cost. In: Bulletin of Kerala Mathematics Association, 1 (1). pp. 82-96.

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The authors consider a rather general stochastic hybrid system formed by a switching diffusion (a pair consisting of a diffusion and a pure jump process that affects the coefficients of the diffusion) that may jump between different regimes whenever the diffusive part hits some predetermined subsets of the state space. It is shown how the switching diffusion can be represented by a system driven by a Wiener process and a Poisson random measure and this system is controlled by a continuous nonanticipative control. The jumps between regimes can in turn be controlled by a discrete set of controls affecting a predetermined impulsive-type map. The control (continuous and discrete) is chosen so as to minimize an infinite horizon discounted cost criterion. Hamilton-Jacobi-Bellman type equations are derived, existence and uniqueness of a classical solution is discussed and a verification theorem is proved. Computational aspects are not considered.

Item Type: Journal Article
Publication: Bulletin of Kerala Mathematics Association
Publisher: Kerala Mathematics Association
Additional Information: Copyright of this article belongs to Kerala Mathematics Association.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 01 Feb 2008
Last Modified: 27 Aug 2008 13:10
URI: http://eprints.iisc.ac.in/id/eprint/12906

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