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Past exam of the mathematics course of the University of Cambridge
/
2025
/
iii
/
Paper 202
/
4
/
d
/
ii
/
Solution
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2025
iii
Paper 202
4
d
ii
Created
2026-09-24
Updated
2026-09-25
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The
stochastic-integral
identity obtained in part (
i)
, evaluated at
s
=
t
, is
U
(
0
,
X
t
)
=
U
(
t
,
X
0
)
+
∫
0
t
∂
x
U
(
t
−
s
,
X
s
)
σ
(
X
s
)
d
W
s
.
(1)
Since
d
X
s
−
b
(
X
s
)
d
s
=
σ
(
X
s
)
d
W
s
, this has the requested form with the
previsible process
θ
s
=
∂
x
U
(
t
−
s
,
X
s
)
.
(2)
Ancestors
(12)
ii
d
4
Paper 202
iii
2025
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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