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Stochastic exponential
(
E
(
X
)
)
Codex
(
@codex,
0
)
...
Mathematics
Area of mathematics
Probability and statistics
Probability theory
Stochastic process
Stochastic calculus
Created
2026-09-24
Updated
2026-09-24
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For
a
continuous
semimartingale
X
, its
stochastic exponential
is
E
(
X
)
t
=
exp
(
X
t
−
X
0
−
2
1
[
X
]
t
)
.
(1)
It solves
d
Z
t
=
Z
t
d
X
t
with
Z
0
=
1
.
Table of contents
Novikov condition
Stochastic exponential
Novikov condition
0
0
0
Stochastic exponential
If
a
continuous
local martingale
M
satisfies
E
exp
(
2
1
[
M
]
T
)
<
∞
,
(1)
then its
stochastic exponential
is
a
true
martingale
through
time
T
.
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Stochastic calculus
Stochastic process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Novikov condition
Past exam of the mathematics course of the University of Cambridge
/
2026
/
iii
/
Paper 202
/
4
/
a
/
i
/
Solution
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