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Geometric Brownian motion
(
d
X
t
=
μ
X
t
d
t
+
σ
X
t
d
B
t
)
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Probability and statistics
Probability theory
Stochastic process
Stochastic calculus
Stochastic differential equation
Itô diffusion
2026-09-28
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Geometric
Brownian motion
has the explicit strong solution
X
t
=
X
0
exp
(
σ
B
t
+
(
μ
−
2
1
σ
2
)
t
)
.
(1)
Ancestors
(9)
Itô diffusion
Stochastic differential equation
Stochastic calculus
Stochastic process
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 202
/
5
/
d
/
Solution
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