In article <[EMAIL PROTECTED]>,
Mouli <[EMAIL PROTECTED]> 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.
There is, but it is far more complicated. For the
general random walk with p_k being the probability
of a step of size k, consider s_j to be the probability
of stopping at the right boundary starting at j. Then
s_j = \sum p_k*s_{j+k}
with the boundary conditions s_j = 1 at the right
boundary or beyond, and s_j = 0 at the left boundary
or beyond. It is the "beyond" which makes a simple
soution not possible.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Deptartment of Statistics, Purdue University
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
.
.
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