MINIMUM CONTRAST ESTIMATORS FOR PIECEWISE DETERMINISTIC MARKOV PROCESSES

The main goal of this paper is to study the minimum contrast estimator (MCE) approach for the parameter estimation problem of piecewise deterministic Markov processes (PDMPs), associated to adaptive control problems. It is assumed that the control acts continuously on the jump intensity lambda and on the transition measure Q of the process, as well as on the costs, and that these parameters depend on an unknown parameter i3*. * . One of our objective is to introduce a minimum contrast estimator (i3n)n is an element of N n ) n is an element of N for the family of PDMPs. Sufficient conditions are then presented to ensure that (i3n)n is an element of N n ) n is an element of N is a strongly consistent estimator of i3*. * . It should be noticed that PDMPs are characterized by a deterministic motion punctuated by random jumps (either spontaneous or due to the flow touching a boundary), which brings new challenges in the analysis of the problem. The paper is concluded with a numerical example for the adaptive discounted control of PDMPs.