M-estimator and its weak consistency for a (2, 1) random walk in a parametric random environment. Issue 3 (3rd July 2019) - Wang, Hua-Ming; Zhang, Meijuan
Abstract: Consider a (2, 1) random walk in an i.i.d. random environment, whose environment involves certain parameter. We construct an M -estimator for the environment parameter which can be written as functionals of a multitype branching process with immigration in a random environment (BPIRE). Because the offspring distributions of the involved multitype BPIRE are of the linear fractional type, the limit invariant distribution of the multitype BPIRE can be computed explicitly. As a result, we get the weak consistency of the M -estimator. Our result is a generalization of Comets et al. [ Stochastic Process. Appl. 2014, 124, 268–288].