218
DOC.
7
PROBABILITY CALCULUS
\2
J
J-X
FY
S(n)F
+ f2
dF
|
dS^.-.dS^
ds("
(13)
n
-m
S(n)F
+ f2
dF
s(n)
+Z2
dlogF
dS(1)...
(nj)
asn) ds(n
But
n
S(")F
+
f
dF
dSM
n n
-I
F
j\
s(n)2
+fY^n
s(n
dF
dS(v...
dS(n'\
0 0
dS(n
or,
if
we
integrate
by
parts
the
second
summand and
take
into account
that
at
infinity
we
must have
F
=
0,
n
=|
s(n2
-
f
•«1
dS(1)...
dS(ni.
0
However,
this
expression
vanishes
because
J
FSW2dSm...
dS{n}
is nothing
else
but
the
average
value
S(n)2,
which
we
derived
in
the
last
section,
for the
case
when
only
a
single
S is
being
considered;
for the latter
it follows from
equation
(10)
that
? =f.
On the
other
hand,
integration
by
parts
yields