ABSTRACT

Fact: Every orthogonal sequence of continuous local martingales can be transformed into a multivariate sequence of independent Brownian motions by rescaling time for each of the martingales via its associated predictable process.

Fact: Given a simple multivariate point process, the multivariate point process obtained by rescaling each process according to its compensator is a sequence of independent Poisson processes, each having intensity 1.

Question: Can a marked point process be transformed into a compound Poisson process with unit total rate and a fixed mark distribution?