ABSTRACT
A parametric family of models for a stochastic process is called an exponential family if for every t > 0, the likelihood function corresponding to the process observed continuously over the time interval [0, t] has the structure of an exponential family We now discuss asemimartingale approach for the study of such families following Kuchler and Sorensen [6]. We have seen earlier that a semimartingale is the sum of a local martingale and a process with bounded variation. The local martingales generalize the class of martingales, whereas the class of semimartingales covers almost all stochastic processes. Let us first discuss some examples of stochastic processes where the likelihood function belongs to an exponential family.
