ISSN 1812-3368. ȼɟɫɬɧɢɤ ɆȽɌɍ ɢɦ. ɇ.ɗ. Ȼɚɭɦɚɧɚ. ɋɟɪ. «ȿɫɬɟɫɬɜɟɧɧɵɟ ɧɚɭɤɢ». 2012
38
Ɏɨɪɦɭɥɚ ɪɚɫɱɟɬɚ ɩɨɤɚɡɚɬɟɥɹ
l
ȡ (lj)
.
Ⱦɥɹ ɪɚɫɱɟɬɚ ɩɨɤɚɡɚɬɟɥɹ ɞɨ-
ɤɚɠɟɦ ɫɥɟɞɭɸɳɟɟ ɭɬɜɟɪɠɞɟɧɢɟ.
Ɍɟɨɪɟɦɚ 1.
ɋɩɪɚɜɟɞɥɢɜɚ ɫɥɟɞɭɸɳɚɹ ɮɨɪɦɭɥɚ
:
1
( )
( ) ,
( )
l
P t dt
l
P
W
W
U W
W
W
³
(3)
ɝɞɟ
( )
P
˜
—
ɜɟɪɨɹɬɧɨɫɬɶ ɛɟɡɨɬɤɚɡɧɨɣ ɪɚɛɨɬɵ ɨɛɴɟɤɬɚ ɜ ɬɟɱɟɧɢɟ
ɜɪɟɦɟɧɢ, ɭɤɚɡɚɧɧɨɝɨ ɜɧɭɬɪɢ ɤɪɭɝɥɵɯ ɫɤɨɛɨɤ
.
Ⱦ ɨ ɤ ɚ ɡ ɚ ɬ ɟ ɥ ɶ ɫ ɬ ɜ ɨ . Ⱦɥɹ ɞɢɫɤɪɟɬɧɨɣ ɱɚɫɬɢ ɜɟɥɢɱɢɧɵ (1), ɪɚɜɧɨɣ
ɜɵɪɚɠɟɧɢɸ ɜɨ ɜɬɨɪɨɣ ɫɬɪɨɤɟ, ɢɦɟɟɦ
(
)
Pr
,
( )
l
P l
l
P
W
]
W
W
W
(4)
ɝɞɟ
Pr( )
˜
—
ɜɟɪɨɹɬɧɨɫɬɶ ɫɨɛɵɬɢɹ, ɡɚɤɥɸɱɟɧɧɨɝɨ ɜɧɭɬɪɢ ɫɤɨɛɨɤ (ɨɬ
ɚɧɝɥ. probability).
ɇɚɣɞɟɦ ɮɭɧɤɰɢɸ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɞɥɹ ɧɟɩɪɟɪɵɜɧɨɣ ɱɚɫɬɢ (1). Ⱦɥɹ
ɷɬɨɣ ɰɟɥɢ, ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ ɭɫɥɨɜɧɵɯ ɜɟɪɨɹɬɧɨɫɬɟɣ, ɢɦɟɟɦ
(
) ( )
Pr
( )
,
( )
l
F x F
x
P
W
W
]
W
W
]
W
W
!
ɝɞɟ
(0, ),
x
l

( )
F x
—
ɮɭɧɤɰɢɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ .
]
Ɉɬɫɸɞɚ ɞɥɹ ɮɭɧɤɰɢɢ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ (1) ɩɨ-
ɥɭɱɢɦ ɫɥɟɞɭɸɳɟɟ ɜɵɪɚɠɟɧɢɟ:
( )
(
) ( )
(
)
.
( )
l
F x F
F
x
P
]
W
W
W
W
W
ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɧɟɩɪɟɪɵɜɧɨɣ ɱɚɫɬɢ (1)
( )
(
)
(
)
,
(0, ),
( )
l
f
x
f
x
x
l
P
]
W
W
W
W

(5)
ɝɞɟ ( )
f x
—
ɩɥɨɬɧɨɫɬɶ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɫɥɭɱɚɣɧɨɣ ɜɟɥɢɱɢɧɵ
.
]
Ɍɨɝɞɚ, ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ (2), ɫ ɭɱɟɬɨɦ (4) ɢ (5) ɢɦɟɟɦ
0
(
)
(
)
( ) (
)
(
)
.
( )
( )
l
l
P l
f
x
l
x
dx
P
P
W
W
U W
W
W
W
W
³
(6)
Ⱦɥɹ ɜɬɨɪɨɝɨ ɫɥɚɝɚɟɦɨɝɨ ɜ ɜɵɪɚɠɟɧɢɢ (6), ɩɪɢɦɟɧɢɜ ɢɧɬɟɝɪɢɪɨɜɚ-
ɧɢɟ ɩɨ ɱɚɫɬɹɦ, ɧɚɣɞɟɦ