Affine diffusions with non-canonical state space

TL;DR

This paper extends the theory of affine diffusions to general state spaces, providing a comprehensive characterization of their behavior with polyhedral and quadratic boundaries, including conditions for invariance and existence.

Contribution

It offers a complete characterization of affine diffusions on non-canonical state spaces, including boundary behavior and existence conditions, expanding beyond the canonical case.

Findings

Characterization of affine diffusions on polyhedral and quadratic state spaces

Necessary and sufficient boundary conditions for invariance

Proof of strong existence and uniqueness under these conditions

Abstract

Multidimensional affine diffusions have been studied in detail for the case of a canonical state space. We present results for general state spaces and provide a complete characterization of all possible affine diffusions with polyhedral and quadratic state space. We give necessary and sufficient conditions on the behavior of drift and diffusion on the boundary of the state space in order to obtain invariance and to prove strong existence and uniqueness.