Конспект лекций по теории случайных процессов. Дронов С.В. - 6 стр.

   , .. 
 

  {    

   -
    :
                         Y                                                   (             )!
                                                                       exp ; 2(t ;xi t )
                             n                                                     �
       P (x 
 :::
 x ) =
         X   �       n       >2(t ; t ; )];      i      i �
                                                                 �=�
                                                                                                 

                             i��                                                i     i;�

  t� = 0.  
 ;
                   !
                   w = AX ,  
                                        0                                 1
                             1 0 0 ::: 0
                                        BBB
                             1 1 0 ::: 0 :                                CCC
                    A=                    @
                            ::: ::: ::: ::: :::                             A
                             1 1 1 ::: 1
:  
, 
 
                   P;                 ;�       ;�
                    !w (X ) = j det Aj PX (A X ):
D
 
  , 
 det A = 1,
                                 0                                                  1
                                 BBB
                            1 0 0 ::: 0 0
                         ;1 1 0 ::: 0 0                                             CCC
                A;� =              BB
                            0 ;1 1 ::: 0 0 
                                          CC
                                    @       :::
                                              0
                                                      ::: ::: :::
                                                       0 0 :::
                                                                        :::
                                                                       ;1 1
                                                                                ::: A


  A;�X = (x�
 x� ; x�
 :::
 xn ; xn;�),
  P;
   !
   w ( x�
 :::
 xn) =
                      Y  n
                        (>2(t ; t ; )];i         i �
                                                         �=�
                                                               expf;(xi ; xi;�)�=2(ti ; ti;�)g)

                     i��

  x� = 0. =, 

     
 

 
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                       w� (t) = w(t) ; tw(1)
 t 2 >0
 1]:
2 
, 
 w�(0) = w�(1) = 0  

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.  t  s.
       K (t
 s) = M(w(t) ; tw(1))(w(s) ; sw(1)) = Mw(t)w(s) ;
                 ; tMw(1)w(s) ; sMw(1)w(t) + stMw�(1):
% , 
  
  


 a Mw�(a) = a,   h > u
         Mw(h)w(u) = M(w(h) ; w(u))w(u) + Mw�(u) = u


 
                K (t
 s) = s ; ts ; st + st = s(1 ; t)
 t  s:

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