Journal of Statistical Physics, Vol. 45, Nos. 5/6, 1986. p. 1031-1047.
We calculate the average residence time r for a particle performing a random walk over a chain of N neighboring sites i= 1,..., N, with decay rates l_i depending on the location of the particle in the chain. Exact results are given for some particular cases, while bounds on T are given for specific initial conditions. In the continuum limit, various results from the literature are recovered or improved upon.