IUNAHY KANI>OM WALKS: ADDENDUM
67
For comparison.
1
1 1 0 1
I
1 1
10,
V(O)V(l) = =
0
and
(17)
( V(O)V( 1 1) = +PY + +(I - P ) ( l - 4 )
= #,
immediately showing the nonstationarity of R ( j ; 11). By proving such identities as
(18)
(X(nt, n - 2)U’(nt, 17 - 2 ) U ( m - 1. n - l)U(m, n ) )
= n ( x ( m , n - 2)U’(/n, I1 - 2 ) )
and far more complicated ones, as for
(X(I?i - 2. I? - 2 ) U ( m - 2, I? - 2)U(I?? - I, n - l)U’(m, / I ) )
a difference equation for (X(rn, 1 1 ) ) may be derived:
I(n -- 81/21 101- 8 - Zk)/21
+ ( 1 - /1)02 1
A Z A + ~ A Z , + J ( ( ~
- / J ) Y ( l i ? ,
I? - 6 - 2k - 2 j )
A - 0
.j 2 n
+ hZ(tti. 17 - 6 - 2k - 2 j ) i
where
Y(I?t, 1 1 ) = ( X ( I i i , n ) ) - / l [ ( X ( m - I, It - 1)) + ( X ( m + 1, I? - l))]
+ (211 - I)(X(,n. I1 - 2 ) )
- (X(n1, I 1 - 4))
Z(W, I I - 2 ) = f[(X(rtl - 1. I I - 3 ) ) + ( X ( W + I , I I - 3 ) ) ]
(5 = 2[/1(I - /J) - 01, A Z k + J = F( -k, +; 3; 40).
Init i d l y
Y ( 0 , 2 ) = Y ( - I. 3 ) = Y ( 1 . 3 ) = 0,
Z ( 0 , 2 ) = -4. Z ( - 1 , 3 ) = 2 ( 1 . 3 ) = - p / 2 .