This paper presents an analysis of the stochastic recursion $$W_{i+1} = [V_iW_i+Y_i]^+$$
W
i
+
1
=
[
V
i
W
i
+
Y
i
]
+
that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model’s stability condition. Writing $$Y_i=B_i-A_i$$
Y
i
=
B
i
-
A
i
, for independent sequences of nonnegative i.i.d. random variables $$\{A_i\}_{i\in {\mathbb N}_0}$$
{
A
i
}
i
∈
N
0
and $$\{B_i\}_{i\in {\mathbb N}_0}$$
{
B
i
}
i
∈
N
0
, and assuming $$\{V_i\}_{i\in {\mathbb N}_0}$$
{
V
i
}
i
∈
N
0
is an i.i.d. sequence as well (independent of $$\{A_i\}_{i\in {\mathbb N}_0}$$
{
A
i
}
i
∈
N
0
and $$\{B_i\}_{i\in {\mathbb N}_0}$$
{
B
i
}
i
∈
N
0
), we then consider three special cases (i) $$V_i$$
V
i
equals a positive value a with certain probability $$p\in (0,1)$$
p
∈
(
0
,
1
)
and is negative otherwise, and both $$A_i$$
A
i
and $$B_i$$
B
i
have a rational LST, (ii) $$V_i$$
V
i
attains negative values only and $$B_i$$
B
i
has a rational LST, (iii) $$V_i$$
V
i
is uniformly distributed on [0, 1], and $$A_i$$
A
i
is exponentially distributed. In all three cases, we derive transient and stationary results, where the transient results are in terms of the transform at a geometrically distributed epoch.