Ergodic Theorems for Dynamic Imprecise Probability Kinematics

2020/03/13 by Caprio, Michele, Mukherjee, Sayan · 2 citations
#37A50 #60A99 #60F15 #60G05 #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2003.06502

Abstract

We formulate an ergodic theory for the (almost sure) limit P^co_E of a sequence (P^co_En) of successive dynamic imprecise probability kinematics (DIPK, introduced in Caprio and Gong, 2021) updates of a set P^co_E0 representing the initial beliefs of an agent. As a consequence, we formulate a strong law of large numbers.

Cited by

• Credal and Interval Deep Evidential Classifications
• Integral Imprecise Probability Metrics

Related

• Dynamic Precise and Imprecise Probability Kinematics
• Nonstandard analysis of the behavior of ergodic means of dynamical systems on very big finite probability spaces
• A Mass Transport Proof of the Ergodic Theorem
• Ergodicity and Mixing of invariant capacities and applications
• Law of large numbers for greedy animals and paths in an ergodic environment