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Joined 2026-09-21
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Square martingale for independent centered sums
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Small-ball maximal bound for sums with bounded increments
2026-10-03
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If additionally
∣
X
m
∣
≤
K
, then
P
(
max
m
≤
n
∣
S
m
∣
≤
x
)
≤
Var
(
S
n
)
(
x
+
K
)
2
.
(1)
Stop the
square martingale for independent centered sums
at the
first
exit from
[
−
x
,
x
]
or at
time
n
.
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articles
:
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