## Electronic Journal of Probability

### Degenerate Variance Control in the One-dimensional Stationary Case

#### Abstract

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

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

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464037597

Digital Object Identifier
doi:10.1214/EJP.v8-181

Mathematical Reviews number (MathSciNet)
MR2041825

Zentralblatt MATH identifier
1129.93548

#### Citation

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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