REFLECTION PRINCIPLES FOR BIASED CORRELATED WALKS - SIMPLE APPLICATIONS

Abstract

The new type of reflection principle applicable to the Laplace transform of the arrival probability for biased walks developed by Khantha and Balakrishnan is extended to the cases of biased correlated walks with absorbing and/or reflecting walls. An exact expression for the mean escape time [t] for the linear discrete walk bounded by absorbing walls at 0 and N is obtained as follows: [t] = N(1 - delta)[2(N - 1)(a - d)]-1[(a(N) + d(N))/(a(N) - d(N)) - (1 + delta)/(a - d)] + delta[(N - 1)(a - d)]-1{1 - [N(a - d)d(N)-1]/(a(N) - d(N))}, where a = 1/2(a + delta + epsilon) and d = 1/2(1 + delta - epsilon), and delta and epsilon are the degrees of correlation and anisotropy, respectively.