Dx = vx � lx.
vn+xln+x
Ex = vn � px = ,
n n
vxlx
1 Dx
= .
Ex Dn+x
n
x b
y
Dy
b � vy-x � px = b � .
y-x
Dx
x
b y, y + 1, . . . , z - 1
z-1
b
Du.
Dx u=y
"
Nx = Du
u=x
b
(Ny - Nz) .
Dx
"
1
�(m) = Dx+h/m,
x
m
Dx h=0
"
1
(m)
Nx = Dx+h/m
m
h=0
(m)
Nx
�(m) = .
x
Dx
(m)
Nx = ą(m) � Nx - �(m) � Dx.
�(m) = ą(m) � �x - �(m)
x
ą(m) � Nx - �(m) � Dx
= .
Dx
m - 1
(m)
Nx <" Nx - � Dx.
=
2m
(m)
Nx <" Nx m - 1
= -
Dx Dx 2m
m-1
Nx - Dx
2m
= ,
Dx
x b/m y, y +
1 2 1
, y + , . . . , z -
m m m
b
(m) (m)
Ny - Nz .
Dx
" "
Ż
Nx = Dx+tdt = Dydy.
0 x
Ż
Nx = ą(") � Nx - �(") � Dx,
id
ą(") = s1| � a1| =
�2
i - �
�(") = .
�2
1
Ż
Nx <" Nx - Dx,
=
2
b
Ż Ż
Ny - Nz .
Dx
m
bx, bx+1, . . . , by, . . . , bx+n-1
m x + n
(y, y + 1)
by � �(m).
y:1|
x+n-1
(apv)x = by � �(m) � Ex.
y-x
y:1|
y=x
x+n-1
(apv)x = by � [ą(m) - �(m)(1 - Ey)] � Ex.
1 y-x
y=x
x+n-1
1
(apv)x = by � [ą(m)Dy - �(m)(Dy - Dy+1)] .
Dx y=x
(m)
(m) (m)
Dy = Ny - Ny+1.
(m)
Dy = ą(m)Dy - �(m)(Dy - Dy+1).
x+n-1
1
(m)
(apv)x = by � Dy .
Dx y=x
x+n-1
(apv)x = by � a(m) � Ex.
y-x
y:1|
y=x
1 1
a(m) = �(m) - (1 - Ey) = ą(m) - �(m) + � [1 - Ey] ,
1 1
y:1| y:1|
m m
x+n-1
1 1
(apv)x = by � ą(m)Dy - �(m) + � [Dy - Dy+1] ,
Dx y=x m
1
(m)
�
Dy = ą(m)Dy - �(m) + � [Dy - Dy+1] .
m
x+n-1
1
(m)
�
(apv)x = by � Dy .
Dx y=x
by = b
(m)
(m)
b/Dx[Nx - Nx+n] by by = y
(m)
Sy
(m)
(m) (m)
Ny = Sy - Sy+1,
"
(m) (m)
Sx = Ny .
y=x
1/m
m
a(m)
Ł
x
1/m
1 1
,
m s1/m|
Ż
t
st|
Ż
1
m s1/m|
Ż
0 �
a(m) =

x,
Ł
x
i(m)
�
a(m) = �

n|.
n|
i(m)
1/m m
1/m
1 1
,
m

1/m|
t


1/m-t|
1
m

1/m|
0 �
�{m} =

x.
x
d(m)
1 = i(m) � a(m) + Ax
Ł
x
1 = d(m) � �{m} + Ax.
x
P
P
" P
0
" P
a
P
P
L
E[L] = 0.
Ż
1 P
L
Ż
l(t) = vt - P �

t|.
T
Ż
L = l(T ) = vT - P �

T |.
E[L] = 0
Ż(Ax)
Ax - P �

x = 0
Ż(Ax) Ax
P = .


x
Var[L] = E[L2],
Ż
P � (1 - vT )
Ż
Var[vT - P �

T |] = Var[vT - ]
�
Ż Ż
P P
= Var vT 1 + -
� �
Ż
P
= Var vT 1 +
�
2
Ż
P
= Var[vT ] 1 +
�
2
Ż
P
2
2
= Ax - Ax 1 + .
�
1 = �

x + Ax
2
2
Ax - Ax
Var[L] = .
(� �

x)2
ŻY ŻY,
bT � vT - P = Z - P
" bt vt
Ż
" P
" Y
" Z
E[bT � vT ]
Ż
P = .
E[Y ]
bT � vT Y
Ż(Ax) Ax
1vT

T | P =


x
1
n

T |, T n
Ż(A1 Ax:n|
1vT P ) =
x:
n|


x:n|


n|, T >n
n 1vT

T |, T n
Ż(Ax:n|) = Ax:n|
P


x:n|
1vn

n|, T >n
1vT

T |, T h
Ż(Ax) Ax
P =
h


x:h|
h 1vT

h|, T >h
n 1vT

T |, T h
Ż(Ax:n|) = Ax:n|
P
1vT

h|, h < T n
h


x:h|
h 1
n 0

T |, T n
1
Ż(Ax:n|) = Ax:n|
P


x:n|
1vn

n|, T >n
1
P
L
L = vK+1 - Px � �K+1| K = 0, 1, . . . .
E[L] = 0
Ax - Px � �x = 0
Ax
Px = .
�x
Var[L] = E[L2],
2
Ax - A2
x
Var[L] = .
(d � �x)2
bK+1 � vK+1 - P � Y = Z - P � Y,
" bk+1 vk+1
" P
" Y
" Z
E[bK+1 � vK+1]
P = .
E[Y ]
bK+1 � vK+1 Y
Ax
1vK+1 �K+1|, K = 0, 1, 2, . . . Px =
�x
A1 n|
n �K+1|, K = 0, 1, . . . , n - 1
x:
1
1vK+1 Px:n| =
�x:n|
�n|, K = n, n + 1, . . .
n 1vK+1 �K+1|, K = 0, 1, . . . , n - 1
Ax:n|
Px:n| =
�x:n|
1vn �n|, K = n, n + 1, . . .
1vK+1 �K+1|, K = 0, 1, . . . , h - 1
Ax
Px =
h
�x:h|
h 1vK+1 �h|, K = h, h + 1, . . .
n 1vK+1 �K+1|, K = 0, 1, . . . , h - 1
Ax:n|
Px:n| =
1vK+1 �h|, K = h, . . . , n - 1
h
�x:h|
h < n 1vn �h|, K = n, n + 1, . . .
1
n 0 �K+1|, K = 0, 1, . . . , n - 1 Ax:n|
1
Px:n| =
�x:n|
1vn �n|, K = n, n + 1, . . .
Ax
P (Ax) = .
�x
i
Ax = Ax,
�
i Ax i
P (Ax) = � = Px.
� �x �
i
1
1
P (Ax:n|) = � Px:n|
�
i
1 1
P (Ax:n|) = � Px:n| + Px:n|.
�
m
Ax Ax
(m) (m)
Px = Px (Ax) =
�(m) �(m)
x x
1
A1 n| Ax:n|
n
x: 1
1(m)
(m)
Px:n| = P (Ax:n|) =
�(m) �(m)
x:n| x:n|
n
Ax:n| Ax:n|
(m)
(m)
Px:n| = P (Ax:n|) =
�(m) �(m)
x:n| x:n|
Ax Ax
(m) (m)
Px = P (Ax) =
h h
�(m) �(m)
h
x:h| x:h|
n
Ax:n| Ax:n|
(m)
(m)
Px:n| = P (Ax:n|) =
h h
�(m) �(m)
x:h| x:h|
h < n
h
Ax:n|
{m}
P (Ax:n|) = .
h
�{m}
x:h|