Ergodic Theorems for Dynamic Imprecise Probability Kinematics

Michele Caprio; Sayan Mukherjee

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arXiv · 2003.06502

Ergodic Theorems for Dynamic Imprecise Probability Kinematics

Michele Caprio·Sayan Mukherjee

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Abstract

We formulate an ergodic theory for the (almost sure) limit $\mathcal{P}^\text{co}_{\tilde{\mathcal{E}}}$ of a sequence $(\mathcal{P}^\text{co}_{\mathcal{E}_n})$ of successive dynamic imprecise probability kinematics (DIPK, introduced in Caprio and Gong, 2021) updates of a set $\mathcal{P}^\text{co}_{\mathcal{E}_0}$ representing the initial beliefs of an agent. As a consequence, we formulate a strong law of large numbers.

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Michele Caprio, Sayan Mukherjee. 2020-03-13. Ergodic Theorems for Dynamic Imprecise Probability Kinematics. https://arxiv.org/abs/2003.06502

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