Леоненко Н.Н., Иванов А.В. Статистический анализ случайных полей
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HBJlHeTCH
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4 .3.1.
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v.n
H8JibI
yCJIOBHH VI, IX
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VII.
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n
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i
cos
(
/...
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o;
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2
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00,
TO npa BbIllOJIHeHI1H yCJIOBHH VII
Ii
IX
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2
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an
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5I
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11
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InO
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00
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r>
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lM
p3cnpeJleJIeHI1
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aHaJIorH'l
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11
4.3.4
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11
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un
on-
V.H.
HeHbl yCJIOBHH VI, IX H XI. T
or-
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51
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C HyJIeBbIM CpeJlHHM H K . cp.
00
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z
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z
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hi
- hzD+
o
+ Y n (v Ih i + h
z
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n
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l
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re
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m
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A )
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B
~
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I
B~)
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I-
1
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Ll n
(Ll-
h) IB (h) 1m.1:.0 IT.H.
..
n OCKOJlbKy;
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sup
I
B~
)
(h) I
~
[M (I
/),,1-
1
i
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dX) +
hEK h
+ M (I
Ll/-
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J}2
(
X)
dX)
1/
2 = [j
~
,I
(I
/),,1
+ ILl + K
1)
/2] B (0);
2) M sup I
B~)
(h) I
:=;;;;
M
(I
/),,1-
1
r
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(x) d
X)
==
B (0),
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l
188
h ET, c
JIa60
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00
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ll
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ro
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{xj(h).h
ET}
/
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o
cJl
e.uosa-
TeJlhHOCTb He3aBHCI1
MbiX
n. H.
aenpepusau
x na KOMnaKTe
T c R" CJl
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on
eii , 5lBJl
51
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00
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m
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or
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m Ha C (T),
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n
Teopeaa
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x (h). h ET c
-
cena-
paoensuoe ra yccoscxoe n
OJI
e H
P{supl
x(h)l
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hEr
,ll.JI5I
nexor oporo a > 0 M exp {a
supx
2
(h)} <
00
.
hEr
Cneiicmeue 4.5.J. O Y
CTb
x (h), hE T (T - K
OMll
aKT
B R
n
) -
n. H. uenp
epusa
oe rayccoscsoe n
OJI
e, H
MO,ll.YJIb
rp
sa (0, u
o]
-
ero
BbI6
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H M
O,ll.YJlb.
Tor jta
,ll.J5I
nex
or
oporo
a>
0
M exp
{
a~2}
<
00
, rne ; = sup (I x (h
(1))
- x (h(2
»)
1/
0<
Ih(\Lh(
2)1
"u,
f
cp
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(l
) - h(2)
I)).
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... B ca
MO
M
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eJle, lJ
~
lJ
11
, CJlenO
Ba
TeJIbHO, cenapacensaoe
ra yccoscxoe n
OJI
e ;
(h)
= (x (h(l
»)
- x (h(2
»))
/
cp
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h(I
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11'
2) I),
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ET
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h(2)
I
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u
}
n. H. or
pa
nn-
o
sene •
Cnenyiouiee yT
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pmneHHe
51
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H.
Teopeaa
4.5.4 [45]. O Y
CT
b x (h), II ET (T -
KOM
naKT Il R
n
)
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rens
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OJI
e H n
JI
5I
h
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), h(2)ET
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l,
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0 H k] <
00
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2
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I
I-
s
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.
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cp
yHKUH
5I
cp
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Il
og u
1-(
s- J+e)12 na (0, u
o]
(u
o
E (0. 1)
--
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or
opoe 'lH
CJI
O)
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B
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ar
a
rs.
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e 11 BbIn
OJIH
eH
O npennonoscenne
XII I. Mo
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u
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l
e
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00
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or)
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~
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0
{P(
lor
l), h, h +
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E
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1
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U
o
II
u.
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1
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00;
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MlJ6+
6
<
00,
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2
+
4
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0
<
00
n.Jl
5I
nexor oporo
a>
o.
O
YCTb
wlf (x) =
u
~
)
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(\) =
1-.,
1-.(
2' =
I-.
n
(I-.
- h),
j
t-~)
(h) =
190
=-=
I
/),,1-
1
~
w~
)
(x) dx, i =
1,2;
p (1) (h(l), h(
2»
) =
Mz
~
)
(h(l
»)
x
f,(i
l
x
z~
)
(h(~
»)
= 1.61-
2
I MW ( 1) (x(l
»)
W ) (xi
2
») dxi
l)d
x
(2),
i = 1, 2,
h
h(2
t.
(l )
~(1
)
=
I-.
x a,
~(
2)
=
(.6
n
(.6
-
h(I»))
x
(.6
n
(.6
_ h(
2»))
.
Baeneu C
JIY
'laiiHble
nOJl51
m
1 2
X~
)
(II) = m
/
(B~
)
(h) - B (h)) =
m-
l12
l}
Jzi
i)
(h), hEK,
;= 1
X
~
)
(h) =
m
l!~
(
B~)
(h) - I
~
/
-1
1.6 n
(.6
- h) IB (h) 1=
m
l
=
m-
/2 ~ it-X)(h) , h EK
i= 1
Bep
051TH
OCTHble
Mepbl
na C (K), COO
TBe
TcTBylO
UJ.
He n
OJI
5IM
x
~
i
,
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~
t~),
a rayccoscxs a n
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5IM
X(i)
C HyJIeBblM Cpe
nm
lM
H K.
~
)
.
p(i) (h(l), h(
2»)
0603Ha'lHM
~t
(i
)
.
Teopexa 4.5.5.
ECJI
H
Bbin
OJI
HeHO
yC
JIO
B
He
XII I, TO
flo
~
)
=>
flo(l)
·
EC
JllI
MHO>KeCTB
O
/').
BbInyK
JIO
, Bb
InOJIHe
HO
XIII, H B
m - )OO
Y
CJI
OIl
HH (6) a= 2, TO II
~t~
)
'*
flo(2l
, m
-
~
00
.
... 1.
OYCT
b ILl
~
u
o
' To
r-
na no
yCJIOBH
IO
XIII
I
z
~
)
(h + 't) -
z
~
)
(h) I
~
I
.6
1-
1
IIs(x) II £(x + II
-+
-c)
-
t,
- £(x + h) Idx +IB (h + r ) - B (h) I
~
~
(110I
/').
,-I
)Is(x) 1dx + MlJoIs(0) I)
cP
( I1:
I)
. .
0 0
HepaBeH
CTB
y
I'
ensnepa
M (l lJo
1/')./-
1J1s(x) I dx
r
~
(
M
lJ~+O
)2/(2+
~
)
X
t,
X (M (1
.6
1-
1
JIs(x) IdxY
+4
/~t<2+
~)
~
(M'!l
~
+O)
2
!
(
2
+
~
)
X
t,
X (M Is(0)
1
2+4
/~)~
/
(
2
+6
)
<
00.
C
JIe
.n.
OBaT
e.7JbH
O,
K
nOJIHM
XJ (h) =
{to
l)(h), h EK n
pHM
eH
HM
a
TeD-
peM
a 4.5 .2,
TaK
K3K
ee YC
JI
OBHlO ynO
BJI
eTB
OpH
eT c. B.
~
1
(1)
=
191
=
'11
0I
~
I-
I
~
1
~
(X)
Idx +
MYlo
I
1;
(0) I·
Il
osr ca y
/-L
~
)
==>
/-L
(I
), m__
DO.
~
2. A HaJIOrHQHO (4.1.1)
Ii
(4.1.2) nOJIy 4aeM
1
z
~)
(h + 't) -
z~
)
(h) I
~
I
~
1- 1
~
11;
(X)
1
11;
(X + h +
1")
-
~
-
~
(X + h) Idx + 1B (h + T)- B (h) I+
+ It.\ [- I
~
IUh (x) Idx + IB (h) II
~
/- 1IM
(~
-
l:)I·
6.
n((
~
-
h
-
t)
e(
~
-
h
l)
n YCTh d = maxIX I, N = [dlu
o]
+ 1. T Or)l,3 no
YCJlOBI1IO
XIII
X E
~
Ii
(4.5.1) n. H.
I
~
\
-
I
Iu
-;
(x) Idx
~
(Ncp
(u
o
)
no
+ 1
1;
(0)
[)Z
X
~
6.
n
«
~
-
h
-
t
)
8
(
~
-
Iz
»
)
x 1
~
e
(~-
T)
1
~
2k. I
~
I
-l
/n
(Ncp
(U
o
)
flo + 1
1;
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)Z
[r I;
IB (h) II
~
I-
I I
~
e
(~-
-c
) I
~
2/
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(0) [
~
,
-I
/It I
-c
\.
n0
3T OMY n. H.
I
l ~)
(h +
rc)
- ti ) (h) I
~
(1
1(1
) +
1P
l)
cp
( I
1"
I),
r.ue
11(2) = 2k. I
~
I- l/n s
up
(u
lcp
(u)) ((N
q>
(U
o
)
11
0 + [£(0)
1)2+
B (0)).
CJle
-
u~uo
noa
arens
no, nOJIe
l
~)
y.n.O
BJIeTB
Op51eT
YCJlOBlI
51
M reopeau 4.5.2,
eCJI
I1
M1
16
< 00 H M 1
1;
(0)I' <
00
. •
3aAte'ialW e 4,5.1,
v'13
noxasare.tscrsa reopeaa 4.5.5 nOH
51
T-
so, 'lTO ycn
osne
Bhm YKJIOCTI1
~
MO)KHO 3aMe Hl1Tb yCJIOBHeM
su
p cp-I (
11"
I) 1
~
e
(~
- r) 1< 00.
(4.5.3)
ITI
:;;u,
n YCJIO
BlIH
X
111
n
pucyrcra
yer
rp
ynao
npoaepaea
oe
Tpe
60
-
uauue unrerpnpyevocra c. B. 110' Ecnn
1;
(x) - rayccoscxoe no-
.ne, TO 3TY
Tpy
.n.HOCT
h :'IO)KHO
npe
ono
ners
Ii
nOJIY4
li
Tb 60
JI
ee 3a·
KO!l4eHHOe yTBep' K
.n.
eHHe 0 CJIa60H CX
O.n.
I1MOCTH Mep
/-L
~
i,
qeM
T
eo
p eMa 4.5.5.
Teopesia 4.5.6.
OYC
Tb !;
(x),
x E
~
+ K -
raycco
acxo
e fl . H.
nenpepusnoe nOJIe,
ocnanaiouiee
Bhl
60poQ
HhlM M
O.n.
ylICM
cp
(u),
U E[
O,
u
o]
' KOTOpoe
yn
oa
nernopaer
ny
axry
(a) yC
JI0I3I151
XIlI.
Tor
zi
a
/-L~
)
=>
/-L
(I).
ECJIH,
xpo
ae
sror
o, cnpasenn aao (4.5.3), TO
'
.l.
~1
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t-t~
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51
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~
(h
(I»)
-
~
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2))
I
/cp
(Ih(l) - h(2)
I)))
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<
00.
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192
n 0 3TOMY M
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nOJlO)KHB
110
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~
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O
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P)
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li
o
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~
(x), x E
~
-
f-
l(
- cenapaoensnoe
onaoponnoe rayccoscxoe
n
OJI
e Il
.n.Jl
51
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o
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II nexoropux
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00
~
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'(;)
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2
-
e
.
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l
(
l),
m
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00 .
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00
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h
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2
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O}
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211}.
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10
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411)
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l
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j
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2
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2
h.
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