Here's a little meditation on Feller (and his being dead) that I wrote in 1999 http://www.kothreat.com/1999.06.26.htm On Sun, Jun 17, 2012 at 11:00 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
I shouldn't think William Feller is on this list either, unless Rich has been scouting for talent in unexpected locations: according to Wikipedia, he died in 1970! http://en.wikipedia.org/wiki/William_Feller
WFL
On 6/17/12, Dan Asimov <dasimov@earthlink.net> wrote:
I don't think William Feller is on this list, but according to him, the probability p(n) of first hitting -1 at the nth step is
p(n) = bin(n, (n-1)/2) / (n * 2^n)
where the binomial coefficient should be taken as 0 for n even -- so p(2k) = 0, which is obvious anyway.
The generating function for these probabilities is shown to be
G(s) = (1 - sqrt(1-s^2)) / s
from which G'(1) = oo. Which shows that as Michael said, the expected time to reach -1 is oo. (I found this to be rather surprising.)
--Dan
Michael wrote: << Surely many people on this list know more than I do about the distribution of times at which the random walker first hits -1.
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