2019/07/24 by Thorsten Schmidt, Schmidt, Thorsten, Stefan Tappe +3
Economics, Econometrics and Finance · Mathematics · #60H10 #60J25 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1907.10337
openalex publication_date 2019/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada-Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results.