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For:
Guérin H
, Renaud J.
Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view.
ADV APPL PROBAB
2016;
48
:274-97. [DOI:
10.1017/apr.2015.17
]
[
Citation(s) in
RCA
: 10
]
[
Impact Index Per Article: 1.3
]
[
Reference Citation Analysis
]
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[Indexed: 11/05/2022]
Number
Cited by Other Article(s)
1
Landriault D
, Li B, Lkabous MA, Wang Z. Bridging the first and last passage times for Lévy models.
Stoch Process Their Appl
2023. [DOI:
10.1016/j.spa.2022.12.005
]
[
Citation(s) in
RCA
: 0
]
[
Impact Index Per Article: 0
]
[
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[Indexed: 12/23/2022]
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2
Sojourn Times of Gaussian Processes with Trend.
J THEOR PROBAB
2019. [DOI:
10.1007/s10959-019-00934-9
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.2
]
[
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[Indexed: 10/26/2022]
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3
Occupation times of alternating renewal processes with Lévy applications.
J Appl Probab
2019. [DOI:
10.1017/jpr.2018.86
]
[
Citation(s) in
RCA
: 1
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/05/2022]
Abstract
Abstract
In this paper we present a set of results relating to the occupation time α(
t
) of a process
X
(·). The first set of results concerns exact characterizations of α(
t
), e.g. in terms of its transform up to an exponentially distributed epoch. In addition, we establish a central limit theorem (entailing that a centered and normalized version of α(
t
)∕
t
converges to a zero-mean normal random variable as
t
→∞) and the tail asymptotics of ℙ(α(
t
)∕
t
≥
q
). We apply our findings to spectrally positive Lévy processes reflected at the infimum and establish various new occupation time results for the corresponding model.
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4
Fluctuations of Omega-killed spectrally negative Lévy processes.
Stoch Process Their Appl
2018. [DOI:
10.1016/j.spa.2017.10.018
]
[
Citation(s) in
RCA
: 13
]
[
Impact Index Per Article: 2.2
]
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[Indexed: 11/18/2022]
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5
Czarna I
, Renaud JF. A note on Parisian ruin with an ultimate bankruptcy level for Lévy insurance risk processes.
Stat Probab Lett
2016. [DOI:
10.1016/j.spl.2016.02.018
]
[
Citation(s) in
RCA
: 8
]
[
Impact Index Per Article: 1.0
]
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[Indexed: 11/29/2022]
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