Abstract
We consider statistical experiments associated with a Lévy process
X
=
X
t
t
≥
0
observed along a deterministic scheme
i
u
n
,
1
≤
i
≤
n
. We assume that under a probability
ℙ
θ
, the r.v.
X
t
,
t
>
0
, has a probability density function
>
o
, which is regular enough relative to a parameter
θ
∈
0
,
∞
. We prove that the sequence of the associated statistical models has the LAN property at each
θ
, and we investigate the case when
X
is the product of an unknown parameter
θ
by another Lévy process
Y
with known characteristics. We illustrate the last results by the case where
Y
is attracted by a stable process.