Catalan Numbers, Riccati Equations and Convergence

TL;DR

This paper explores the relationship between Catalan numbers and Riccati equations in the context of stochastic differential games on infinite networks, focusing on convergence properties via Fourier analysis.

Contribution

It introduces a novel connection between Catalan numbers and Riccati equations in stochastic game theory, analyzing convergence through Fourier transforms.

Findings

Established a link between Catalan numbers and Riccati equations.

Proved convergence of Catalan functions using Fourier transforms.

Analyzed finite and infinite Riccati systems in networked stochastic games.

Abstract

We analyze both finite and infinite systems of Riccati equations derived from stochastic differential games on infinite networks. We discuss a connection to the Catalan numbers and the convergence of the Catalan functions by Fourier transforms.