Multifractals
Tau(q) is a decreasing function of q
Differentiating
p
i
q
r
i
tau(q)
= 1
with respect to q gives
p
i
q
r
i
tau(q)
(ln(p
i
) + ln(r
i
) dtau/dq) = 0
Solving for dtau/dq,
dtau/dq = -(
p
i
q
r
i
tau(q)
(ln(p
i
)))/(
p
i
q
r
i
tau(q)
(ln(r
i
)))
Because each
p
i
q
> 0,
r
i
tau(q)
> 0,
ln(p
i
) < 0,
and
ln(r
i
) < 0,
we see
dtau/dq < 0.
Return to
the range of alpha values
.
