It is not unusual that where , V, Z are real random variables, V is independent of Z and . An intriguing feature [...] Read more.
It is not unusual that
are real random variables, V
is independent of Z
. An intriguing feature is that
for each Borel set
, namely, the probability distribution of the limit
is a mixture of centered Gaussian laws with (random) variance
. In this paper, conditions for
are given, where
is the total variation distance between the probability distributions of
. To estimate the rate of convergence, a few upper bounds for
are given as well. Special attention is paid to the following two cases: (i)
is a linear combination of the squares of Gaussian random variables; and (ii)
is related to the weighted quadratic variations of two independent Brownian motions.