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Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 201
/
4
/
b
/
i
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Past exam of the mathematics course of the University of Cambridge
2024
iii
Paper 201
4
b
2026-09-24
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Solution
i
Solution
0
0
0
i
The
strong law for Brownian motion
gives
B
t
/
t
→
0
almost surely
. Therefore
t
B
t
=
t
B
t
−
μ
⟶
−
μ
<
0
(1)
almost surely
, and hence
B
t
→
−
∞
almost surely
.
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b
4
Paper 201
iii
2024
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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