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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 202
/
6
/
b
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Mathematics course of the University of Cambridge
Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 202
6
2026-09-28
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Solution
b
Solution
0
0
0
b
The
Itô product rule
for
e
λ
t
X
t
gives
d
(
e
λ
t
X
t
)
=
e
λ
t
d
B
t
.
(1)
Therefore the
Ornstein-Uhlenbeck process
has the explicit form
X
t
=
x
e
−
λ
t
+
∫
0
t
e
−
λ
(
t
−
s
)
d
B
s
.
(2)
Ancestors
(10)
6
Paper 202
iii
2022
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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