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Cost‐efficient monitoring of continuous‐time stochastic processes based on discrete observations
Author(s) -
Yoshioka Hidekazu,
Yaegashi Yuta,
Tsujimura Motoh,
Yoshioka Yumi
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2559
Subject(s) - mathematical optimization , ambiguity , computer science , stochastic optimization , linkage (software) , discrete time stochastic process , mathematics , continuous time stochastic process , biochemistry , chemistry , gene , programming language
Planning a cost‐efficient monitoring policy of stochastic processes arises from many industrial problems. We formulate a simple discrete‐time monitoring problem of continuous‐time stochastic processes with its applications to several industrial problems. A key in our model is a doubling trick of the variables, with which we can construct an algorithm to solve the problem. The cost‐efficient monitoring policy balancing between the observation cost and information loss is governed by an optimality equation of a fixed point type, which is solvable with an iterative algorithm based on the Feynman‐Kac formula. This is a new linkage between monitoring problems and mathematical sciences. We show regularity results of the optimization problem and present a numerical algorithm for its approximation. A problem having model ambiguity is presented as well. The presented model is applied to problems of environment, ecology, and energy, having qualitatively different target stochastic processes with each other.