Decay times in one-dimensional chains (Q1094001)

We calculate the average residence time \(\tau\) for a particle performing a random walk over a chain of N neighboring sites \(i=1,...,N\), with decay rates \(\lambda_ i\) depending on the location of the particle in the chain. Exact results are given for some particular cases, while bounds on \(\tau\) are given for specific initial conditions. In the continuum limit, various results from the literature are recovered or improved upon.