The iterated Galton-Watson process

Journal of Applied Probability

Volumn 33, Issue 4, 1996, Pages 949-959

  Gawel, Boleslaw ^a   Kimmel, Marek ^b  

^a UNIVERSITY OF SILESIA   (Poland)

^b Rice University   (United States)

Author keywords

DNA; Galton Watson process

Indexed keywords

EID: 0030375333     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200100385     Document Type: Article

References (13)

1. ATHREYA, K. B. AND NEY, P. E. (1972) Branching Processes. Springer, New York.
2. AXELROD, D. E. AND KIMMEL, M. (1996) Stochastic models of expanding triplet repeats in hereditary diseases. In preparation.
3. CASKEY, C. T., PIZUTTI, A., FU, Y.-H., FENWICK, JR. R. G. AND NELSON, D. L. (1992) Triplet repeat mutations in human disease. Science 256, 784-789.
4. CAVALIER-SMITH, T. (1985) Introduction: the evolutionary significance of genome size. In The Evolution of Genome Size. ed. T. Cavalier-Smith. Wiley, New York. pp 1-36.
5. CHUNG, K. L. (1974) A Course in Probability Theory. 2nd edn. Academic Press, New York.
6. FU, Y.-H., KUHL, D. P. A., PIZZUTTI, A., PIERETTI, M., SUTCLIFFE, J. S., RICHARDS, S., VERKEERK, A. J. M. H., HOLDEN, J. J. A., FENWICK, JR. R. G., WARREN, S. T., OOSTRA, B. A., NELSON D. L. AND CASKEY, C. T. (1992) Variation of the CGG repeat at the Fragile X site results in genetic instability: Resolution of the Sherman paradox. Cell 67, 1047-1058.
7. IMBERT, D., KRETZ, C., JOHNSON, K. AND MANDEL, J.-L. (1993) Origin of the expansion mutation in myotonic dystrophy. Nature Genet. 4, 72-76.
8. KIMMEL, M., STIVERS, D. N. (1994) Time-continuous branching walk models of unstable gene amplification. Bull. Math. Biol. 56, 337-358.
9. KUHL, D. P. A. AND CASKEY, C. T. (1993) Trinucleotide repeats and genome variation. Current Opinion Genet. Develop. 3, 404-407.
10. MARX, J. (1993) New colon cancer gene discovered. Science 260, 751-752.
11. MOSIG, G. (1987) The essential role of recombination in phage T4 growth. Ann. Rev. Genet. 21, 347-371.
12. REDMAN, J. B., FENWICK, JR. R. G., FU, Y.-H., PIZZUTTI, A. AND CASKEY, C. T. (1993) Relationship between parental trinucleotide GCT repeat length and severity of myotonic dystrophy in offspring. JAMA 269, 1960-1965.
13. RICHARDS, R. I. AND SUTHERLAND, G. R. (1992) Dynamic mutations: A new class of mutations causing human disease. Cell 70, 709-712.