Ɍɚɤɢɦ ɨɛɪɚɡɨɦ
&
ɛɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɚɩɪɢɨɪɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɞɜɭɯ
'
ɭɝɥɨɜɚɹ ɫɯɟɦɚ ɞɢɫɬɚɧɰɢɨɧɧɨɝɨ ɡɨɧɞɢɪɨɜɚɧɢɹ ɧɟ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶ
'
ɡɨɜɚɧɚ ɩɪɢ ɨɛɧɚɪɭɠɟɧɢɢ ɧɟɮɬɹɧɵɯ ɡɚɝɪɹɡɧɟɧɢɣ ɧɚ ɧɟɪɨɜɧɨɣ ɦɨɪɫɤɨɣ
ɩɨɜɟɪɯɧɨɫɬɢ
(
Ⱥɩɪɢɨɪɧɚɹ ɢɧɮɨɪɦɚɰɢɹ
&
ɤɨɬɨɪɚɹ ɦɨɠɟɬ ɛɵɬɶ ɷɮɮɟɤɬɢɜɧɨ ɢɫɩɨɥɶ
'
ɡɨɜɚɧɚ ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɡɚɞɚɱɟ
&
ɷɬɨ ɞɚɧɧɵɟ ɨ ɫɤɨɪɨɫɬɢ ɢ ɧɚɩɪɚ
'
ɜɥɟɧɢɢ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ ɧɚɞ ɢɫɫɥɟɞɭɟɦɨɣ ɚɤɜɚɬɨɪɢɟɣ
(
Ɍɚɤɚɹ ɢɧɮɨɪɦɚ
'
ɰɢɹ ɥɟɝɤɨ ɞɨɫɬɭɩɧɚ ɢ ɞɨɫɬɚɬɨɱɧɨ ɬɨɱɧɚ
"
ɨɫɨɛɟɧɧɨ ɜ ɫɥɭɱɚɟ ɩɪɢɛɪɟɠɧɵɯ
ɪɚɣɨɧɨɜ ɦɨɪɟɣ
#(
Ɋɚɫɫɦɨɬɪɢɦ ɫɥɭɱɚɢ
&
ɤɨɝɞɚ ɚɩɪɢɨɪɧɚɹ ɢɧɮɨɪɦɚɰɢɹ ɩɪɟɞɫɬɚɜɥɟɧɚ ɜ
ɪɚɡɥɢɱɧɨɦ ɜɢɞɟ
(
ɋɥɭɱɚɣ ɧɚɥɢɱɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɨ ɫɤɨɪɨɫɬɢ ɢ ɧɚ
'
ɩɪɚɜɥɟɧɢɢ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ ɧɚɞ ɢɫɫɥɟɞɭɟɦɨɣ ɚɤɜɚɬɨɪɢɟɣ
(
Ⱥɥɝɨ
'
ɪɢɬɦ ɨɛɧɚɪɭɠɟɧɢɹ ɧɟɮɬɹɧɵɯ ɡɚɝɪɹɡɧɟɧɢɣ ɜ ɷɬɨɦ ɫɥɭɱɚɟ ɜɤɥɸɱɚɟɬ ɜ ɫɟ
'
ɛɹ ɫɥɟɞɭɸɳɢɟ ɷɬɚɩɵ
(
+(
Ɉɩɪɟɞɟɥɟɧɢɟ ɜɟɥɢɱɢɧɵ ɞɢɫɩɟɪɫɢɢ ɧɚɤɥɨɧɨɜ
o
2
x
ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ
ɩɨɥɟɬɚ ɧɨɫɢɬɟɥɹ
(
ɋɢɝɧɚɥɵ
P
0
&
P
x
&
ɪɟɝɢɫɬɪɢɪɭɟɦɵɟ ɩɪɢɟɦɧɢɤɨɦ ɥɚɡɟɪ
'
ɧɨɝɨ ɥɨɤɚɬɨɪɚ ɜ ɞɜɭɯɭɝɥɨɜɨɣ ɫɯɟɦɟ ɡɨɧɞɢɪɨɜɚɧɢɹ
&
ɢɫɩɨɥɶɡɭɸɬɫɹ ɞɥɹ
ɜɵɱɢɫɥɟɧɢɹ ɫɥɟɞɭɸɳɟɣ ɜɟɥɢɱɢɧɵ
4
P
x
P
0
= exp
μ
a
0
,
5
q
2
x
q
2
z
o
2
x
¶
.
(
,
)
Ⱦɚɥɟɟ ɩɨ ɢɡɜɟɫɬɧɨɣ ɜɟɥɢɱɢɧɟ
P
x
/P
0
ɜɵɱɢɫɥɹɟɬɫɹ ɜɟɥɢɱɢɧɚ ɞɢɫɩɟɪ
'
ɫɢɢ ɧɚɤɥɨɧɨɜ
o
2
x
ɜɞɨɥɶ ɧɚɩɪɚɜɥɟɧɢɹ ɩɨɥɟɬɚ ɧɨɫɢɬɟɥɹ
(
Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɞɢɫɩɟɪɫɢɢ
o
2
y
ɧɟɨɛɯɨɞɢɦɚ ɢɧɮɨɪɦɚɰɢɹ ɨ ɫɤɨɪɨɫɬɢ
ɢ ɧɚɩɪɚɜɥɟɧɢɢ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ
(
,(
Ɉɩɪɟɞɟɥɟɧɢɟ ɫɜɹɡɢ ɞɢɫɩɟɪɫɢɣ ɧɚɤɥɨɧɨɜ
o
2
x
&
o
2
y
ɫɨ ɫɤɨɪɨɫɬɶɸ ɢ ɧɚ
'
ɩɪɚɜɥɟɧɢɟɦ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ ɢ ɫ ɧɚɥɢɱɢɟɦ ɧɟɮɬɹɧɵɯ ɡɚɝɪɹɡɧɟɧɢɣ
(
ȼɟ
'
ɥɢɱɢɧɵ
o
2
x
&
o
2
y
ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ
U3W4
1
o
2
x
=
cos
2
o
2
u
+
sin
2
o
2
}
;
(
-
)
1
o
2
y
=
cos
2
o
2
}
+
sin
2
o
2
u
;
(
.
)
ɡɞɟɫɶ
o
2
u
ɢ
o
2
}
ɞɢɫɩɟɪɫɢɢ ɧɚɤɥɨɧɨɜ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ ɜɞɨɥɶ ɢ ɩɨ
'
ɩɟɪɟɤ ɧɚɩɪɚɜɥɟɧɢɹ ɜɟɬɪɚ
5
ɭɝɨɥ ɦɟɠɞɭ ɨɫɶɸ
x
"
ɧɚɩɪɚɜɥɟɧɢɟɦ ɩɨ
'
ɥɟɬɚ ɧɨɫɢɬɟɥɹ
#
ɢ ɧɚɩɪɚɜɥɟɧɢɟɦ ɜɟɬɪɚ
(
Ⱦɢɫɩɟɪɫɢɢ
o
2
u
&
o
2
}
ɡɚɜɢɫɹɬ ɨɬ ɫɤɨɪɨɫɬɢ ɩɪɢɜɨɞɧɨɝɨ ɜɟɬɪɚ ɢ ɧɚɥɢɱɢɹ
ɧɟɮɬɹɧɵɯ ɡɚɝɪɹɡɧɟɧɢɣ ɧɚ ɦɨɪɫɤɨɣ ɩɨɜɟɪɯɧɨɫɬɢ
(
,, CMMH *,-0'-3--(
ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ
(
ɇ
(
ɗ
(
Ȼɚɭɦɚɧɚ
(
ɋɟɪ
(
ɉɪɢɛɨɪɨɫɬɪɨɟɧɢɟ
( ,**/(
ʋ
+
