Large deviations for Generalized Polya Urns with non-binary increments

TL;DR

This paper extends the sample-path large deviation principle for urn models to include non-binary increments, broadening the theoretical framework for analyzing generalized Polya urns with multiple possible increment values.

Contribution

It modifies existing large deviation results to accommodate urn processes with multi-valued increments, enhancing the theoretical understanding of generalized Polya urns.

Findings

Extended large deviation principles to non-binary increments.

Provided a sketch for modifying existing theorems.

Broadened applicability of urn process analysis.

Abstract

In this paper we show how to extend the Sample-Path Large Deviation Principle for the urn model of Hill, Lane and Sudderth to the case in which the increment of the urn is not a binary variable. In particular, we sketch how to modify the Theorem 1 given in [Stochastic Processes and their Applications 127 (2017) 3372-3411] to include also urn processes with increments taking more than two values.