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Bernstein concentration inequality for products of sub-Gaussian variables
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)
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Mathematics
Area of mathematics
Probability and statistics
Sub-Gaussian random variable
Sub-exponential random variable
Product of sub-Gaussian random variables is sub-exponential
2026-09-28
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For independent identically distributed
pairs
(
U
i
,
V
i
)
whose coordinates are sub-Gaussian with
parameter
σ
/4
,
Bernstein's inequality
applied to the centered products gives
P
(
n
1
∑
i
=
1
n
{
U
i
V
i
−
E
(
U
i
V
i
)}
≥
t
)
≤
2
exp
(
−
σ
2
(
σ
2
+
t
)
2
n
t
2
)
.
(1)
Ancestors
(7)
Product of sub-Gaussian random variables is sub-exponential
Sub-exponential random variable
Sub-Gaussian random variable
Probability and statistics
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 205
/
4
/
Solution
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