Electronic Journal of Probability

Degenerate Variance Control in the One-dimensional Stationary Case

Daniel Ocone and Ananda Weerasinghe

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We study the problem of stationary control by adaptive choice of the diffusion coefficient in the case that control degeneracy is allowed and the drift admits a unique, asymptotically stable equilibrium point. We characterize the optimal value and obtain it as an Abelian limit of optimal discounted values and as a limiting average of finite horizon optimal values, and we also characterize the optimal stationary strategy. In the case of linear drift, the optimal stationary value is expressed in terms of the solution of an optimal stopping problem. We generalize the above results to allow unbounded cost functions.

Article information

Electron. J. Probab., Volume 8 (2003), paper no. 24, 27 p.

First available in Project Euclid: 23 May 2016

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Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control
Secondary: 60G35: Signal detection and filtering [See also 62M20, 93E10, 93E11, 94Axx]

stochastic control stationary control degenerate variance control


Ocone, Daniel; Weerasinghe, Ananda. Degenerate Variance Control in the One-dimensional Stationary Case. Electron. J. Probab. 8 (2003), paper no. 24, 27 p. doi:10.1214/EJP.v8-181. https://projecteuclid.org/euclid.ejp/1464037597

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