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Past exam of the mathematics course of the University of Cambridge
/
2021
/
iii
/
Paper 202
/
4
/
d
/
Solution
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Past exam of the mathematics course of the University of Cambridge
2021
iii
Paper 202
4
d
2026-09-28
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The
Doléans-Dade exponential
X
t
=
exp
(
M
t
−
2
1
[
M
]
t
)
(1)
is
a
positive
continuous local martingale
with
X
0
=
1
, and part
c
shows
X
t
→
0
. Apply part
a
with
a
=
e
y
:
P
(
t
≥
0
sup
{
M
t
−
2
1
[
M
]
t
}
>
y
)
=
P
(
t
sup
X
t
>
e
y
)
=
e
−
y
.
(2)
Ancestors
(11)
d
4
Paper 202
iii
2021
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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