Advances in Applied Probability
- Adv. in Appl. Probab.
- Volume 45, Number 1 (2013), 164-185.
Bayesian quickest detection problems for some diffusion processes
We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the weighted likelihood ratios hit stochastic boundaries depending on the current observations. The proof is based on the reduction of the initial problems into appropriate three-dimensional optimal stopping problems and the analysis of the associated parabolic-type free-boundary problems. We provide closed-form estimates for the value functions and the boundaries, under certain nontrivial relations between the coefficients of the observable diffusion.
Adv. in Appl. Probab., Volume 45, Number 1 (2013), 164-185.
First available in Project Euclid: 15 March 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 34K10: Boundary value problems
Secondary: 62C10: Bayesian problems; characterization of Bayes procedures 62L15: Optimal stopping [See also 60G40, 91A60] 60J60: Diffusion processes [See also 58J65]
Gapeev, Pavel V.; Shiryaev, Albert N. Bayesian quickest detection problems for some diffusion processes. Adv. in Appl. Probab. 45 (2013), no. 1, 164--185. doi:10.1239/aap/1363354107. https://projecteuclid.org/euclid.aap/1363354107