Asymptotic behaviours of pressure functionals and statistical representations of the coefficients (Integrated Research on Random Dynamical Systems and Multi-Valued Dynamical Systems)

Abstract

We study an asymptotic behaviour of the pressure functional P(ϕ+tψ)＝P(ϕ) ＋p₁t+p₂t²+・・・+Pnt^n+0(t^n) (t→0) with potentials ϕ and ψ on a countable Markov shift X. We show that if the transition matrix of X is finitely primitive, the potentials ϕ and ψ are real-valued locally Holder continuous functions on X, and a sufficient condition for an asymptotic expansion of t→P(ϕ+tψ) is satisfied, then the 3-th coefficient p₃ of this expansion has a limit representation which looks like the asymptotic variance p2 well. The form of the coefficient pq (q≥ 4) is also investigated under a special condition for似ial condition for ϕ