Конспект лекций по теории случайных процессов. Дронов С.В. - 15 стр.


  
    +)  
 

 . 7
  -

 )
 
  
 (6)           

  (8k)(8 c�
 :::
 ck 2 C) (8t�
 :::
 tk 2 >A
 B ])
                                                     X X c c8 K (t ; t )  0:
                                                     k   k
                                                                 i j     i   j   (8)
                                                     i�� j��

       
 4.       
  (8). #

  1)   K (0)   {      
            
             
,

  2)   (8t) K (t) = K (;t)Q
  3)   (8t) jK (t)j K (0):


 . 1). - (8) k = 1
 c� = 1
 t� = 0
 
  K (0)  0.
    2). 
 
 
 )
 
  
 k = 2
 t� =
t
 t� = 0,    , 
  
  
 
  
 c�
 c�
  


               (jc�j� + jc�j�)K (0) + c�c8�K (t) + c8�c�K (;t)  0:              (9)
-   
  

 
                 1  
   , 

                         (8a 2 C) aK (t) + a8K (;t) 2 R:
  a = a� + ia�
 K (t) = K� + iK�
 K (;t) = K� + iK�: ,
 , 
  
    +

                           =m(aK (t) + a8K (;t)) = 0

 
, 
  
  
     a�
 a� 
 
 -
 

                  a�(K� + K� ) + a� (K� ; K� ) = 0


  K� = ;K�
 K� = K�, 
 
 
 
.
   3). - (8) k = 2
 t� = t
 t� = 0
 c� = ;K (0)
 c� = K (t): ,
 
  (9)     , 

        (K �(0) + jK (t)j�)K (0) ; K (0)jK (t)j� ; K (0)jK (t)j�  0


 
   

  "   

                              K � (0)   ; jK (t)j�  0:
D 
.

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