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Citation(s) in
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9
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Cited by Other Article(s)
1
Piau D
. Addendum to ‘Quasi-renewal estimates’ for modelling DNA replication.
J Appl Probab
2016. [DOI:
10.1239/jap/1014843098
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.3
]
[
Reference Citation Analysis
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[Indexed: 11/18/2022]
Abstract
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2
Piau D
. Quasi-renewal estimates.
J Appl Probab
2016. [DOI:
10.1239/jap/1014842284
]
[
Citation(s) in
RCA
: 5
]
[
Impact Index Per Article: 0.6
]
[
Reference Citation Analysis
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[
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[Indexed: 11/18/2022]
Abstract
We show that the solution of a quasi-renewal equation with an exponential distribution of the renewals converges at infinity and we compute explicitly the limit, hence generalizing the classical renewal theorem. We apply this result to a stochastic model of DNA replication introduced by Cowan and Chiu (1994).
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3
On the time behaviour of Okazaki fragments.
J Appl Probab
2006. [DOI:
10.1017/s0021900200001789
]
[
Citation(s) in
RCA
: 0
]
[
Impact Index Per Article: 0
]
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[Indexed: 11/06/2022]
Abstract
We find explicit analytical formulae for the time dependence of the probability of the number of Okazaki fragments produced during the process of DNA replication. This extends a result of Cowan on the asymptotic probability distribution of these fragments.
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4
Lachal A
. Some probability distributions in modeling DNA replication.
ANN APPL PROBAB
2003. [DOI:
10.1214/aoap/1060202839
]
[
Citation(s) in
RCA
: 5
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/19/2022]
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5
Cowan R
. Ch. 4. Stochastic models for DNA replication.
HANDBOOK OF STATISTICS
2003. [DOI:
10.1016/s0169-7161(03)21006-3
]
[
Citation(s) in
RCA
: 3
]
[
Impact Index Per Article: 0.1
]
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[Indexed: 12/30/2022]
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6
A new discrete distribution arising in a model of DNA replication.
J Appl Probab
2001. [DOI:
10.1017/s0021900200018908
]
[
Citation(s) in
RCA
: 2
]
[
Impact Index Per Article: 0.1
]
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[Indexed: 11/06/2022]
Abstract
During DNA replication, small fragments of DNA are formed. These have been observed experimentally and the mechanism of their formation modelled mathematically. Using the stochastic model of Cowan and Chiu (1992), (1994), we find the probability distribution of the number of fragments. A new discrete distribution arises. The work has interest as an application of the recent theory on quasirenewal equations in Piau (2000).
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7
Cowan R
. A new discrete distribution arising in a model of DNA replication.
J Appl Probab
2001. [DOI:
10.1239/jap/1005091038
]
[
Citation(s) in
RCA
: 4
]
[
Impact Index Per Article: 0.2
]
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[Indexed: 11/18/2022]
Abstract
During DNA replication, small fragments of DNA are formed. These have been observed experimentally and the mechanism of their formation modelled mathematically. Using the stochastic model of Cowan and Chiu (1992), (1994), we find the probability distribution of the number of fragments. A new discrete distribution arises. The work has interest as an application of the recent theory on quasirenewal equations in Piau (2000).
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MESH Headings
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Grants
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Affiliation(s)
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8
Addendum to ‘Quasi-renewal estimates’ for modelling DNA replication.
J Appl Probab
2000. [DOI:
10.1017/s0021900200018374
]
[
Citation(s) in
RCA
: 0
]
[
Impact Index Per Article: 0
]
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[Indexed: 11/06/2022]
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9
Quasi-renewal estimates.
J Appl Probab
2000. [DOI:
10.1017/s0021900200015412
]
[
Citation(s) in
RCA
: 4
]
[
Impact Index Per Article: 0.2
]
[
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[Indexed: 11/08/2022]
Abstract
We show that the solution of a quasi-renewal equation with an exponential distribution of the renewals converges at infinity and we compute explicitly the limit, hence generalizing the classical renewal theorem. We apply this result to a stochastic model of DNA replication introduced by Cowan and Chiu (1994).
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