derived from a function v that takes
both positive and negative values, or, more generally, for a CAF A=B-C
that is the
difference of PCAFs, it is easily seen that Kac's moment formula
remains valid
provided
at each of the n successive integrations involved
in computing 
, 
,
the integral is absolutely convergent for each 
,
as is the final integration with respect to 
. Such formulae are
used, for example, in [58, 42, 44] to study the asymptotics
of differences 
of local times, as 
.