Tree-Indexed Autoregressive Processes and Related Stochastic Fixed Point Equations

• Activity Number: 538
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Anand Vidyashankar*+ and Jeffrey F. Collamore
• Companies: George Mason University and University of Copenhagen
• Keywords: tree-indexed process ; large deviations ; autoregressive processes ; stochastic fixed point equations ; Galton_watson process ; martingales

Abstract

Tree-indexed autoregressive (AR) processes arise in several applications such as cell biology, aging, insurance, and finance. These processes are formed by constructing AR processes along the rays of a Galton-Watson tree. In this model, the random variables on the edges are correlated if they share a common ancestor. An analogue of the classical martingale that arise in branching random walk can be constructed for these processes and their limit satisfies a stochastic fixed point equation. This talk will describe: (i) necessary and sufficient conditions for non-degeneracy of the martingale limit, (ii) the tail behavior of the associated stochastic fixed point equation, and (iii) precise large deviations for the occupation measure. (Joint work with Jeffrey Collamore).