=
1 +
s
pq
2
E
[
g
(
p
−
1
, q
)
E
(
ε
pq
)
−
s
pq
E
[
g
(
p
−
1
, q
)
E
[
ε
pq
I
(
ε
pq
<
<
−
a
10
X
p
−
1
,q
)
|
A
pq
]] +
o
(1) =
=
−
s
pq
E
g
(
p
−
1
, q
)
−
a
10
X
p
−
1
,q
Z
−∞
tF
0
(
t
)
dt
+
o
(1) =
=
−
s
pq
E
g
(
p
−
1
, q
)
0
Z
−∞
tF
0
(
t
)
dt
+
o
(1) =
=
s
pq
E
E
[
g
(
p
−
1
, q
)] +
o
(1) =
s
pq
E
2
−
m
(
q
−
1)
−
p
+1
+
o
(1)
,
a
10
→
0
.
Лемма 2 доказана.
Из лемм 1 и 2 следует, что
E
g
(
p, q
) =
=
1
2
E
g
(
p
−
1
, q
) +
a
10
s
pq
F
0
(0)
E
s
p
−
1
,q
E
2
−
m
(
q
−
1)
−
p
+2
+
o
(1) +
o
(
a
10
) =
=
1
2
E
g
(
p
−
1
, q
) =
a
10
s
pq
s
p
−
1
,q
F
0
(0)
E
2
−
m
(
q
−
1)
−
p
+2
+
o
(
a
10
)
.
Полученная рекуррентная формула для
E
g
(
p, q
)
с начальным условием
(5) дает
E
g
(
p, q
) = 2
−
m
(
q
−
1)
−
p
"
1 +
a
10
4
F
0
(0)
E
p
X
i
=2
q
X
j
=1
s
ij
s
i
−
1
,j
#
+
o
(
a
10
)
.
Так как
P
{
S
=
s
|
a
}
=
E
g
(
m, n
)
, теорема 1 доказана.
СПИСОК ЛИТЕРАТУРЫ
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H e l e n T. N a u g h t o n. FDI in space: Spatial autoregressive relationships in
foreign direct investment // European Economic Review. – Vol. 51, issue 5, July
2007. – P. 1303–1325.
2. D o n g p i n g Z h u A. A. (Louis) Beex. Robust Spatial Autoregressive Modeling
for Hardwood Log Inspection. Journal of Visual Communication and Image
Representation. – Vol. 5, issue 1, March 1994. – P. 41–51.
3. C h e l l a p p a R., S h a r m a G. Two-dimensional spectral estimation using
spatial autoregressive models // Acoustics, Speech, and Signal Processing, IEEE
International Conference on ICASSP’83. – V. 8, Apr. 1983. – P. 855–858.
4. T j o s t h e i m D. Statistical spatial series modeling // Adv. in Appl. Probab., 1978.
– V. 10. – P. 130–154.
5. T j o s t h e i m D. Statistical spatial series modelling II: Some futher results on
unilateral processes // Adv. in Appl. Probab., 1983. – V. 10. – P. 562–584.
122
ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. “Естественные науки”. 2009. № 2
