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Citation(s) in
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5
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Cited by Other Article(s)
1
On an integral equation for first-passage-time probability densities.
J Appl Probab
2016. [DOI:
10.1017/s0021900200024694
]
[
Citation(s) in
RCA
: 20
]
[
Impact Index Per Article: 2.5
]
[
Reference Citation Analysis
]
[
Abstract
]
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]
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[Indexed: 11/06/2022]
Abstract
We prove that for a diffusion process the first-passage-time p.d.f. through a continuous-time function with bounded derivative satisfies a Volterra integral equation of the second kind whose kernel and right-hand term are probability currents. For the case of the standard Wiener process this equation is solved in closed form not only for the class of boundaries already introduced by Park and Paranjape [15] but also for all boundaries of the type S(I) = a + bt ‘/p (p ∼ 2, a, b E ∼) for which no explicit analytical results have previously been available.
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2
A note on the evaluation of first-passage-time probability densities.
J Appl Probab
2016. [DOI:
10.1017/s0021900200097084
]
[
Citation(s) in
RCA
: 10
]
[
Impact Index Per Article: 1.3
]
[
Reference Citation Analysis
]
[
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]
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[Indexed: 11/06/2022]
Abstract
A procedure is indicated to estimate first-passage-time p.d.f.'s through varying boundaries for a class of diffusion processes that can be transformed into the Wiener process by rather general transformations. Although this procedure is adapted to Durbin's [4] algorithm, it could be extended to other existing computation methods.
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3
Stochastic barriers for the Wiener process.
J Appl Probab
2016. [DOI:
10.1017/s0021900200023482
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.3
]
[
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[Indexed: 11/06/2022]
Abstract
Let {
W
(
t
), 0 ≦
t
< ∞} be the standard Wiener process. The probabilities of the type
P
[sup
0≦
t
≦
T
W
(
t
) −
f
(
t
) ≧ 0] have been extensively studied when
f
(
t
) is a deterministic function. This paper discusses the probabilities of the type
P
{sup
0≦
t
≦
T
W
(
t
) − [
f
(
t
) +
X
(
t
)] ≧ 0} when
X
(
t
) is a stochastic process. By taking compound Poisson processes as
X
(
t
), the paper gives procedures for finding such probabilities.
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4
Sacerdote L
. Asymptotic behaviour of ornstein-uhlenbeck first-passage-time density through periodic boundaries.
ACTA ACUST UNITED AC
1990. [DOI:
10.1002/asm.3150060106
]
[
Citation(s) in
RCA
: 7
]
[
Impact Index Per Article: 0.2
]
[
Reference Citation Analysis
]
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]
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[Indexed: 11/09/2022]
Abstract
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5
Loader C
, Deely J. Computations of boundary crossing probabilities for the wiener process.
J STAT COMPUT SIM
1987. [DOI:
10.1080/00949658708810984
]
[
Citation(s) in
RCA
: 7
]
[
Impact Index Per Article: 0.2
]
[
Reference Citation Analysis
]
[
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]
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[Indexed: 10/23/2022]
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