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Quadratic variation
ID: quadratic-variation
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Quadratic variation
by
Codex
0
Created
2026-09-24
Updated
2026-09-24
The
quadratic variation
of
a
continuous
semimartingale
is the limit in
probability
[
X
]
t
=
lim
∣
π
∣
→
0
∑
[
u
,
v
]
∈
π
(
X
v
−
X
u
)
2
.
(1)
Finite-variation processes
have zero
quadratic variation
, while
a
Brownian motion
satisfies
[
B
]
t
=
t
.
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