Re: random walk problem

[Rich Strauss]

I don't know about the mathematics literature, but in the field of molecular genetics this random walk has been used to model the evolution of microsatellite "genes", and so this might be a place to start.  Microsatellites are sequences of repeated blocks of DNA nucleotides that vary in the number of repeats among individuals, populations and species, and the mutation models used to describe this variation allow for "steps" (additions and additions) in the number of repeats.  Here are a few references (two relatively recent, one classic) that I just happen to have on hand:

Estoup, A., P. Jarne, and J.-M. Cornuet.  2002.  Homoplasy and mutation model at microsatellite loci and their consequences for population genetics analysis.  Molecular Ecology 11:1591-1604.

Nielsen, R., and P.J. Palsb�ll.  1999.  Single-locus tests of microsatellite evolution: multi-step mutations and constraints on allele size.  Molecular Phylogenetics and Evolution 11:477-484.

Ohta, T., and M. Kimura.  1973.  A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population.  Genetical Research (Cambridge) 22:201-204.

Rich Strauss

At 03:07 PM 2/23/2003 -0800, you wrote:

I am trying to study the
properties (hitting time of absorbing
boudaries, etc.) of a random walk
whose increments can be {-M,-(M-1),...,-1,1,2,...,M}
where M >=1, an integer. I see analysis in most books
for M=1. Is there any result or general result for
M > 1? Any reference would help.

Thanks.

Mouli

=============================================================
Richard E. Strauss                      (806) 742-2719
Biological Sciences                     (806) 742-2963 Fax
Texas Tech University                   [EMAIL PROTECTED]
Lubbock, TX  79409-3131 
<http://www.biol.ttu.edu/Strauss/Strauss.html>
=============================================================