메뉴 건너뛰기




Volumn 32, Issue 1 A, 2004, Pages 337-364

Immortal branching markov processes: Averaging properties and pcr applications

Author keywords

Dna amplification; Error prone pcr; Estimation; Galton watson process; Markov branching process; Mean field approximation; Mutation rate; Polymerase chain reaction (pcr)

Indexed keywords


EID: 2142708291     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1078415838     Document Type: Article
Times cited : (14)

References (22)
  • 1
    • 0010876723 scopus 로고
    • Large deviation rates for branching processes I. Single type case
    • ATHREYA, K. B. (1994). Large deviation rates for branching processes I. Single type case. Ann. Appl. Probab. 4 779-790.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 779-790
    • Athreya, K.B.1
  • 3
    • 0002244969 scopus 로고
    • Martingale convergence in the branching random walk
    • BIGGINS, J. (1977). Martingale convergence in the branching random walk. J. Appl. Probab. 14 25-37.
    • (1977) J. Appl. Probab. , vol.14 , pp. 25-37
    • Biggins, J.1
  • 4
    • 84862345069 scopus 로고    scopus 로고
    • Genetical and statistical aspects of polymerase chain reactions
    • Univ. Dortmund
    • BRUNNERT, M., MU¨LLER, O. and URFER, W. (2000). Genetical and statistical aspects of polymerase chain reactions. Technical Report 6/2000, Univ. Dortmund.
    • (2000) Technical Report , vol.6 , Issue.2000
    • Brunnert, M.1    Müller, O.2    Urfer, W.3
  • 5
    • 0013325511 scopus 로고
    • A new look at convergence of branching processes
    • GREY, D. (1980). A new look at convergence of branching processes. Ann. Probab. 8 377-380.
    • (1980) Ann. Probab. , vol.8 , pp. 377-380
    • Grey, D.1
  • 6
    • 0000823566 scopus 로고
    • Mutations induced during the polymerase chain reaction
    • HAYASHI, K. (1990). Mutations induced during the polymerase chain reaction. Technique 2 216-217.
    • (1990) Technique , vol.2 , pp. 216-217
    • Hayashi, K.1
  • 7
    • 0042804110 scopus 로고
    • An invariance principle and some convergence rate results for branching processes
    • HEYDE, C. C. and BROWN, B. M. (1971). An invariance principle and some convergence rate results for branching processes. Z. Wahrsch. Verw. Gebiete 20 271-278.
    • (1971) Z. Wahrsch. Verw. Gebiete , vol.20 , pp. 271-278
    • Heyde, C.C.1    Brown, B.M.2
  • 8
    • 0032998669 scopus 로고    scopus 로고
    • Enrichment polymerase chain reaction for the detection of Ki-ras mutations: Relevance of Taq polymerase error rate, initial DNA copy number, and reaction conditions on the emergence of false-positive mutant bands
    • JACOBS, G., TSCHOLL, E., SEK, A., PFREUNDSCHUH, M., DAUS, H. and TRU¨MPER, L. (1999). Enrichment polymerase chain reaction for the detection of Ki-ras mutations: Relevance of Taq polymerase error rate, initial DNA copy number, and reaction conditions on the emergence of false-positive mutant bands. J. Cancer Res. Clin. Oncol. 125 395-401.
    • (1999) J. Cancer Res. Clin. Oncol. , vol.125 , pp. 395-401
    • Jacobs, G.1    Tscholl, E.2    Sek, A.3    Pfreundschuh, M.4    Daus, H.5    Trümper, L.6
  • 9
    • 0000415075 scopus 로고
    • A new martingale in branching random walk
    • JOFFE, A. (1993). A new martingale in branching random walk. Ann. Appl. Probab. 3 1145-1150.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 1145-1150
    • Joffe, A.1
  • 10
    • 0024524024 scopus 로고
    • Polymerase chain reaction: Replication errors and reliability of gene diagnosis
    • KRAWCZAK, M., REISS, J., SCHMIDTKE, J. and ROSLER, U. (1989). Polymerase chain reaction: Replication errors and reliability of gene diagnosis. Nucleic Acids Res. 17 2197-2201.
    • (1989) Nucleic Acids Res. , vol.17 , pp. 2197-2201
    • Krawczak, M.1    Reiss, J.2    Schmidtke, J.3    Rosler, U.4
  • 11
    • 0008984822 scopus 로고    scopus 로고
    • A simple path to Biggins' martingale convergence for branching random walk
    • (K. B. Athreya and P. Jagers, eds.). Springer, New York
    • LYONS, R. (1997). A simple path to Biggins' martingale convergence for branching random walk. In Classical and Modern Branching Processes (K. B. Athreya and P. Jagers, eds.) 217-221. Springer, New York.
    • (1997) Classical and Modern Branching Processes , pp. 217-221
    • Lyons, R.1
  • 12
    • 0001318023 scopus 로고
    • Estimation of errors in the polymerase chain reaction
    • MARUYAMA, I. N. (1990). Estimation of errors in the polymerase chain reaction. Technique 2 302-303.
    • (1990) Technique , vol.2 , pp. 302-303
    • Maruyama, I.N.1
  • 13
    • 23544463277 scopus 로고    scopus 로고
    • Harmonic moments and large deviation rates for supercritical branching processes
    • Univ. Georgia
    • NEY, P. E. and VIDYASHANKAR, A. N. (2001). Harmonic moments and large deviation rates for supercritical branching processes. Technical Report Stat2001-5, Univ. Georgia.
    • (2001) Technical Report , vol.STAT2001-5
    • Ney, P.E.1    Vidyashankar, A.N.2
  • 14
    • 0016702992 scopus 로고
    • Non-parametric estimation in the Galton-Watson process
    • PAKES, A. G. (1975). Non-parametric estimation in the Galton-Watson process. Math. Biosci. 26 1-18.
    • (1975) Math. Biosci. , vol.26 , pp. 1-18
    • Pakes, A.G.1
  • 15
    • 17944368179 scopus 로고    scopus 로고
    • Processus de branchement en champ moyen et re´action PCR
    • PIAU, D. (2001). Processus de branchement en champ moyen et re´action PCR. Adv. in Appl. Probab. 33 391-403.
    • (2001) Adv. in Appl. Probab. , vol.33 , pp. 391-403
    • Piau, D.1
  • 16
    • 0036997797 scopus 로고    scopus 로고
    • Mutation-replication statistics for polymerase chain reactions
    • PIAU, D. (2002). Mutation-replication statistics for polymerase chain reactions. J. Comput. Biol. 9 831-847.
    • (2002) J. Comput. Biol. , vol.9 , pp. 831-847
    • Piau, D.1
  • 17
    • 0025270143 scopus 로고
    • The effect of replication errors on the mismatch analysis of PCR-amplified DNA
    • REISS, J., KRAWCZAK, M., SCHLO & die;SSER, M., WAGNER, M. and COOPER, D. N. (1990). The effect of replication errors on the mismatch analysis of PCR-amplified DNA. Nucleic Acids Res. 18 973-978.
    • (1990) Nucleic Acids Res. , vol.18 , pp. 973-978
    • Reiss, J.1    Krawczak, M.2    Schlösser, M.3    Wagner, M.4    Cooper, D.N.5
  • 19
    • 0029258483 scopus 로고
    • The polymerase chain reaction and branching processes
    • SUN, F. (1995). The polymerase chain reaction and branching processes. J. Comput. Biol. 2 63-86.
    • (1995) J. Comput. Biol. , vol.2 , pp. 63-86
    • Sun, F.1
  • 20
    • 0034100229 scopus 로고    scopus 로고
    • Estimation of the mutation rate during error-prone polymerase chain reaction
    • WANG, D., ZHAO, C., CHENG, R. and SUN, F. (2000). Estimation of the mutation rate during error-prone polymerase chain reaction. J. Comput. Biol. 7 143-158.
    • (2000) J. Comput. Biol. , vol.7 , pp. 143-158
    • Wang, D.1    Zhao, C.2    Cheng, R.3    Sun, F.4
  • 21
    • 0029258947 scopus 로고
    • Modeling the polymerase chain reaction
    • WEISS, G. and VON HAESELER, A. (1995). Modeling the polymerase chain reaction. J. Comput. Biol. 2 49-61.
    • (1995) J. Comput. Biol. , vol.2 , pp. 49-61
    • Weiss, G.1    Von Haeseler, A.2
  • 22
    • 0030807050 scopus 로고    scopus 로고
    • A coalescent approach to the polymerase chain reaction
    • WEISS, G. and VON HAESELER, A. (1997). A coalescent approach to the polymerase chain reaction. Nucleic Acids Res. 25 3082-3087.
    • (1997) Nucleic Acids Res. , vol.25 , pp. 3082-3087
    • Weiss, G.1    Von Haeseler, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.