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Tanaka formula
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Area of mathematics
Probability and statistics
Probability theory
Stochastic process
Stochastic calculus
Itô formula
Created
2026-09-24
Updated
2026-09-24
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For
a
continuous
semimartingale
X
,
∣
X
t
∣
=
∣
X
0
∣
+
∫
0
t
sgn
(
X
s
)
d
X
s
+
L
t
0
(
X
)
,
(1)
where
L
0
(
X
)
is the
local time of a semimartingale
at zero.
Table of contents
Local time of a semimartingale
Tanaka formula
Local time of a semimartingale
(
L
t
a
(
X
)
)
0
0
0
Tanaka formula
Local
time
measures
how intensely
a
semimartingale
visits
a
level. For
a
continuous
semimartingale
it appears
as
the increasing correction term in the
Tanaka formula
.
Ancestors
(8)
Itô formula
Stochastic calculus
Stochastic process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Local time of a semimartingale
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 202
/
2
/
d
/
Solution
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