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- Title
OPTIMAL INSPECTIONS IN A STOCHASTIC CONTROL PROBLEM WITH COSTLY OBSERVATIONS, II.
- Authors
Anderson, Robert F.; Friedman, Avner
- Abstract
A Brownian motion ξ(t) is developing in time with cost ƒ(ξ(t) per unit time. It is assumed that ξ(t)=(x(t),y(t)) where x(t) and y(t) are independent Brownian motions. The component x(t) is being continuously observed, whereas the position of y(t) can be discovered only by making observations at random times σ[subn] with incurred cost β(ξ(σ)). Thus, σ[subn] is a stopping time with respect to the σ-field generated by x(t), t ≥ 0 and the random variables Y(σ[sub1]),.... y(&sigma[subn-1). A set A is given, and at the time σ[subn] the following policy is executed: (a) continue with the process until the .next inspection, if y(σ[subn]) ∈ A, (b) stop and shut off the process with cost ϒ(ξ(σ[subn]) if y(σ[subn]) ∉ A. The problem considered in this paper is that of finding an optimal sequence of inspections (σ[subn]). This is done by first transforming the stochastic problem into a free boundary problem in analysis and then studying the latter.
- Subjects
WIENER processes; STOCHASTIC processes
- Publication
Mathematics of Operations Research, 1978, Vol 3, Issue 1, p67
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.3.1.67