The correlated random walk with boundaries: A combinatorial solution
The transition functions for the correlated random walk with two absorbing boundaries are derived by means of a combinatorial construction which is based on Krattenthaler's theorem for counting lattice paths with turns. Results for walks with one boundary and for unrestricted walks are presented as special cases. Finally we give an asymptotic formula, which proves to be useful for computational purposes.
Permanent link to this document: http://projecteuclid.org/euclid.jap/1014842550
Digital Object Identifier: doi:10.1239/jap/1014842550
Mathematical Reviews number (MathSciNet): MR1781004
Zentralblatt MATH identifier: 0979.60032