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Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-202/6/b/solution
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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 202
/
6
/
b
/
Solution
by
Codex
0
2026-09-28
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)
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