ISSN:
1432-2064

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics

Notes:
Summary We study the distance in variation between probability measures defined on a measurable space (Ω, ℱ) with right-continuous filtration (ℱt)t ≦0. To every pair of probability measures P and $$\tilde P$$ an increasing predictable process $$h = h(P,{\text{ }}\tilde P)$$ (called the Hellinger process) is associated. For the variation distance $$\left\| {P_T - \tilde P_T } \right\|$$ between the restrictions of P and $$\tilde P$$ to ℱ T (T is a stopping time), lower and upper bounds are obtained in terms of h. For example, in the case when $$P_0 = \tilde P_0 $$ , $$2(1 - (E{\text{ }}\exp {\text{ }}( - h_T ))^{1/2} ) \leqq \left\| {P_T - \tilde P_T } \right\| \leqq 4(Eh_T )^{1/2} $$ In the cases where P and $$\tilde P$$ are distributions of multivariate point processes, diffusion-type processes or semimartingales h are expressed explicitly in terms of given predictable characteristics.

Type of Medium:
Electronic Resource