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  • Growth of conditional means  (1)
  • central limit theorem  (1)
  • 1
    Electronic Resource
    Electronic Resource
    An alternative approach to asymptotic results on genetic composition when the population size is varying (1983)
    Springer
    Journal of mathematical biology 18 (1983), S. 163-168 
    Details
    ISSN: 1432-1416
    Keywords: Allelic composition ; Ultimate homozygosity ; Polymorphism ; Growth of conditional means ; Martingale methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract This paper is concerned with methodology for studying the long-term genetic composition of a population of haploid individuals in the case where the population size is varying. A general approach requiring a minimum of assumptions is described based on constructing martingales out of expressions for the means of the numbers of allelic types, conditional on the past. Earlier investigations were based on studying the asymptotic behaviour of the proportion of alleles of a certain type in the population. Several applications demonstrate that the approach suggested in the paper provides results which usefully complement ones obtained previously.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00280664
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  • 2
    Electronic Resource
    Electronic Resource
    On the asymptotic behavior of random walks on an anisotropic lattice (1982)
    Springer
    Journal of statistical physics 27 (1982), S. 721-730 
    Details
    ISSN: 1572-9613
    Keywords: Random walks ; anisotropic lattices ; Brownian motion ; martingale methods ; central limit theorem ; law of the iterated logarithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A random walk on a two-dimensional lattice with homogeneous rows and inhomogeneous columns, which could serve as a model for the study of some transport phemonema, is discussed. Subject to an asymptotic density condition on the columns it is shown that the horizontal motion of the walk is asymptotically like that of rescaled Brownian motion. Various consequences of this are derived including central limit, iterated logarithm, and mean square displacement results for the horizontal component of the walk.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013444
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