Solutions of First Order Linear Partial Differential Equations Related to Urn Models and Central Limit Theorems
Michael Drmota, Mehri Javanian
TL;DR
This paper analyzes first order linear PDEs related to urn models and establishes conditions under which a central limit theorem holds, using the method of characteristics.
Contribution
It provides a new framework connecting PDE solutions to urn models and formulates sufficient conditions for CLT applicability.
Findings
Derived solutions for PDEs in urn model analysis
Established conditions for central limit theorems in this context
Linked PDE methods with probabilistic limit theorems
Abstract
We study first order linear partial differential equations that appear, for example, in the analysis of dimishing urn models with the help of the method of characteristics and formulate sufficient conditions for a central limit theorem.
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Taxonomy
TopicsPolynomial and algebraic computation · Geometric and Algebraic Topology · Geometry and complex manifolds