: D = P - I, I - , , D= ||dij||,
(2.6).
0 < dij < 1, i = j; -1 < dii < 0 i = =1,..., n
(3)
P(k) - P(k-1) = P(k-1) × D (2.7)
(2.7) k- .
Ҳ ʲ в.
1. - , P(k) = P × P×... ×P - .
2. , P(k) = .
3.
= (2.8),
D - , , , , D . , , .
4.
= (2.9),
, , D - , (k) , , D, . D , . , D , .
= (2.10)
(k), k - > 0, .
(2.9) (2.10) , .
5.
= (2.11),
B, - , (2m) (2.8), (2m+1) - (2.10).
, , , ; .
.
, , . .
: , ,
P(k)=P( )= (2.12),
= (P1, P2,..., Pn), (Pm> 0), P1, P2,..., Pn, (0). , - .
, () , . . (k) ( ) (t) ( ) .
,
( ) = ( )´P(2.13)
( )´D = 0 (2.14)
, ,
(2.15)
k P(k) ( ) = (P1, P2,..., Pn).
(0), k P(k) = (P1, P2,..., Pn).
|
|
, - ,
(2.16)
.
6. 3 () 1, 2, 3. . 볺 , 1, 2, 3 . ( ) 볺 1(0)=0,5; 2(0)=0,2; 3(0)=0,3. 볺 , , 1 , 2 3. Pij (i, j = 1, 3), S1, S2, S3, Si - Bi (i = 1, 2, 3),
볺 , , .6. ( ), . | .6 |
. , , . (2.16).
p1+p2+p3 = 1
p = (p1; p2; p3)
,
,