Original scientific paper

Estimation of the killing rate parameter in a diffusion model

Roža Horvat-Bokor ; OTP Bank Nyrt., Ltd. Risk Management, Budapest, Hungary
Miljenko Huzak ; Department of Mathematics, University of Zagreb, Zagreb, Croatia
Nedžad Limić ; Department of Mathematics, University of Zagreb, Zagreb, Croatia

Abstract

We consider a parameter estimation problem for a diffusion with
killing, starting at a point in an open and bounded set. The
infinitesimal killing rate function depends on a control variable
and parameters.
Values of the control variable are known while parameters have unknown values which have to be estimated
from data.
The minimum of three times: the maximum observation time, the first exit time from the open set, and the killing time, is observed.
Instead of the maximum likelihood estimation method we propose and use the minimum $\chi^2$-estimation method that is based on the conditional mean of the data observed before the maximum observation time is reached, and on the frequency of data that are equal to the maximum observation time. We prove that the estimator exists and is consistent and asymptotically normal. The method is
illustrated by an example.

Keywords

diffusion with killing; censored data; minimum $\chi^2$-estimation; random search

Hrčak ID:

82994

URI

https://hrcak.srce.hr/82994

Publication date:

12.6.2012.

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