The martingale theory of jump processes

A jump process is best analyzed by investigating the space of all martingales which are generated by the process. The structure of this space of martingales becomes clear in the martingale representation results. Having understood this structure, one can completely resolve the most important problems in 1) modeling and description, 2) detection or hypothesis testing, and 3) filtering of jump processes. Several exercises are worked out to suggest the power of this approach.