Construction of Exponential Martingales for Counting Processes.

Let Nt be a counting process with continuous compensator At and ft a bounded predictabler process. If Eexp2fNt infinity and Eexp 21 expfA t infinity then it is shown that z exp -integral from 0 to t fudNu - integral from 0 to t exp -fu - 1dAu is a martingale. This is a partial extension of a theorem of Kabanov, Liptser, Shiryaev 1980 who assumed At or but did not assume At is continuous. Keywords Random variables, Stochastic processes, Poisson processes, convergence.