Multi-Dimensional Quality Control Problems and Quasi Variational Inequalities

Robert F. Anderson, Avner Friedman
1978 Transactions of the American Mathematical Society  
A machine can manufacture any one of n m-dimensional Brownian motions with drift A" P$, defined on the space of all paths x(i) G C(J0, oo); Rm). It is given that the product is a random evolution dictated by a Markov process 9(t) with n states, and that the product is P*> when 9 (i) = j, 1 < j < n. One observes the a-fields of x (/), but not of 6 (/). With each product p£> there is associated a cost c.. One inspects 9 at a sequence of times (each inspection entails a certain cost) and stops
more » ... uction when the state 9 = n is reached. The problem is to find an optimal sequence of inspections. This problem is reduced to solving a certain elliptic quasi variational inequality. The latter problem is actually solved in a rather general case. Received by the editors June 13, 1976. AMS (MOS) subject classifications (1970). Primary 62N10, 90B25, 93E20; Secondary 35J99, 60H05, 60H10, 60K30, 90A15, 90E25.
doi:10.2307/1997964 fatcat:jc7diqdfprfjvi5oozrbqxzeyq