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In this paper we derive the log likelihood function for point processes in terms of their stochastic intensities by using the martingale approach. For practical purposes we work with an approximate log likelihood function that is shown to possess the usual asymptotic properties of a log likelihood function. The resulting estimates are strongly consistent and asymptotically normal (under some regularity conditions). As a by-product, a strong law of large numbers and a central limit theorem for martingales in continuous times are derived.

The presence of N-acetylglucosamine is essential for the induced synthesis of N-acetylglucosamine kinase in Candida albicans. The enzyme synthesis stops and its concentration in the cells declines rapidly as soon as N-acetylglucosamine is removed from the medium. Experiments with RNA- and protein-synthesis inhibitors indicate that the appearance of new enzyme activity is dependent on concomitant new protein synthesis and the inducer operates at a transcriptional level.