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Brownian covariance kernel
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Probability and statistics
Probability theory
Random variable
Hilbert-space-valued random variable
Covariance operator
Covariance kernel
2026-09-24
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The
covariance kernel
of standard
Brownian motion
on
[
0
,
1
]
is
c
(
s
,
t
)
=
min
(
s
,
t
)
. Its
integral operator
has
eigenfunctions
2
sin
((
k
−
2
1
)
π
t
)
and
eigenvalues
((
k
−
2
1
)
π
)
−
2
.
Ancestors
(9)
Covariance kernel
Covariance operator
Hilbert-space-valued random variable
Random variable
Probability theory
Probability and statistics
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 225
/
1
/
a
/
i
/
Solution
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