2022/10/30 by Liangang Ma, Ma, Liangang, Mark Pollicott +1
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2210.16794
openalex publication_date 2022/10/30 · openalex created_date 2022/11/06 · openalex updated_date 2026/07/28
The first part of this work is devoted to the study of higher differentials of pressure functions of Hölder potentials on shift spaces of finite type. By describing the differentials of pressure functions via the Central Limit Theorem for the associated random processes, we discover some rigid relationships between differentials of various orders. The rigidity imposes obstructions on fitting candidate convex analytic functions by pressure functions of Hölder potentials globally, which answers a question of Kucherenko-Quas. In the second part of the work we consider fitting candidate analytic germs by pressure functions of locally constant potentials. We prove that all 1-level candidate germs can be realised by pressures of some locally constant potentials, as long as number of the symbolic set is large enough. There are also some results on fitting 2-level germs by pressures of locally constant potentials obtained in the work.