Title: Asymptotic inference for branching random walks with immigration and applications
Authors: Anand Vidyashankar - George Mason University (United States) [presenting]
Abstract: Branching Random Walk with Immigration (BRWI) models and their variants are useful for modeling a variety of physical, technological, biological, and financial phenomena and some of their theoretical properties have recently been studied in the literature. We focus on inference for functionals of the process; Specifically, the Laplace transform (LT) of the BRWI. We establish that there exists an interval, defined through a critical parameter, in which the LT is consistently estimable even if the BRWI process is only partially observed. Additionally, we establish the asymptotic normality of the estimator. Finally, we provide some applications to inference for the cascade generator in the study of conservative cascades.