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Boundary hitting probability from a diffusion scale function
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)
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Probability and statistics
Probability theory
Stochastic process
Stochastic calculus
Stochastic differential equation
Scale function (stochastic processes)
2026-09-28
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If
a
<
x
<
b
and the
diffusion
exits
(
a
,
b
)
almost surely
, optional stopping of the bounded
local martingale
s
(
X
t
∧
τ
)
gives
P
x
(
X
τ
=
a
)
=
s
(
b
)
−
s
(
a
)
s
(
b
)
−
s
(
x
)
,
P
x
(
X
τ
=
b
)
=
s
(
b
)
−
s
(
a
)
s
(
x
)
−
s
(
a
)
.
(1)
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(9)
Scale function (stochastic processes)
Stochastic differential equation
Stochastic calculus
Stochastic process
Probability theory
Probability and statistics
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Hitting-zero classification for a Bessel process
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 202
/
5
/
c
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2023
/
iii
/
Paper 203
/
2
/
b
/
Solution
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