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- W1968699588 abstract "The problem of controlling a noisy process so as to prevent it from leaving a prescribed set has a number of interesting applications. In this paper, new approaches to this problem are considered. First, a risk-sensitive criterion for a stochastic diffusion process model is examined, and it is shown that the value is a classical solution of a related PDE. The qualitative properties of this criterion are favorably contrasted with those of existing criteria in the risk-averse limit. It is proved that in the risk-averse limit the value of the risk-sensitive criterion converges to a viscosity solution of a first-order PDE. It is then demonstrated that the value function of a deterministic differential game is also a viscosity solution to the PDE. This game gives a robust control formulation of the escape time problem and is analogous to H$^{infty}$ control. In particular, the opposing player attempts to push the process out of the prescribed set and suffers an L2 cost for his efforts. Lower bounds on the escape time as a function of this cost are obtained." @default.
- W1968699588 created "2016-06-24" @default.
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- W1968699588 date "1997-11-01" @default.
- W1968699588 modified "2023-10-16" @default.
- W1968699588 title "Risk-Sensitive and Robust Escape Criteria" @default.
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- W1968699588 doi "https://doi.org/10.1137/s0363012995281626" @default.
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