Likelihood Ratio Tests and Applications in 2D Lognormal Diffusions

In a previous work by the authors, maximum likelihood estimators (MLEs) were obtained for the drift and diffusion coefficients characterizing 2D lognormal diffusion models involving exogenous factors affecting the drift term. Such models are well-known to describe properly the behaviour of real phenomena of interest, for instance, in geophysical and environmental studies. The present paper provides the distribution of these MLEs, the Fisher information matrix, and the solution to some likelihood ratio tests of interest for hypotheses on the parameters weighting the relative effect of the exogenous factors.