On the construction of conditional probability densities

Pavel V. Gapeev , Monique Jeanblanc (1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

In this paper, we construct strictly positive conditional probability densities with respect to the given reference filtration in the two cases of a filtration generated by a Brownian motion and a (compound) Poisson process. Then, by means of the results contained in [23], it is possible to construct the associated random times on some extended probability space. Hence, Jacod's equivalence hypothesis, that is, the existence of strictly positive conditional densities for the random times with respect to the reference filtration, is obviously satisfied.

Keywords: Mathematics Subject Classification 2010: Primary 60G44; 60J65; 60G40. Secondary 60G35; 60H10; 91G40 Brownian motion; (compound) Poisson process; conditional probability density process; Jacod's equivalence hypothesis; initial and progressive enlargements of filtrations; Mathematics Subject Classification 2010: Primary 60G44

Domains: Probability [math.PR]

Pavel V. Gapeev, Monique Jeanblanc. On the construction of conditional probability densities. 2022. ⟨hal-03740822⟩