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Planar Brownian annulus hitting probability
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Probability and statistics
Probability theory
Stochastic process
Brownian motion
Planar Brownian motion
Harmonic measure
2026-09-24
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For
planar Brownian motion
started at
x
with
0
<
r
<
∣
x
∣
<
R
,
P
x
(
T
r
<
T
R
)
=
l
o
g
R
−
l
o
g
r
l
o
g
R
−
l
o
g
∣
x
∣
.
(1)
This is optional stopping applied to the
harmonic function
lo
g
∣
x
∣
on the
annulus
.
Ancestors
(9)
Harmonic measure
Planar Brownian motion
Brownian motion
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
/
2024
/
iii
/
Paper 201
/
3
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 202
/
3
/
d
/
i
/
Solution
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