Statistical model uncertainty for state-observation models driven by diffusion process

Abstract

This paper is motivated by the fact that model uncertainty is common-seen in statistics and applied probability. As a response, a likelihood ratio-based approach is presented to statistical detection within a class of state-observation models. Here, the system is driven by some diffusion process while the continuous-time observation process is of additive white noise. The proposed approach can be implemented recursively to compare the competing stochastic systems by fitting the observed historical data. It is superior to the traditional hypothesis test in both theoretical and numerical senses. Moreover, it can be extended to the more general martingale problem setup.