Subadditive Ergodic Theorem for Double Sequences

Vytautas Kazakevičius ()
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Vytautas Kazakevičius: Vilnius University

Journal of Theoretical Probability, 2021, vol. 34, issue 1, 307-330

Abstract: Abstract A functional ergodic theorem is proved for subadditive families of measurable functions $$(h_{k,n}\mid (k,n)\in D)$$ ( h k , n ∣ ( k , n ) ∈ D ) , where $$D\subset {\mathbb {N}}^2$$ D ⊂ N 2 is an additive semigroup and subadditivity means that $$h_{k_1+k_2,n_1+n_2}\le h_{k_1,n_1}+h_{k_2,n_2}\circ f^{n_1}$$ h k 1 + k 2 , n 1 + n 2 ≤ h k 1 , n 1 + h k 2 , n 2 ∘ f n 1 for some measure-preserving transformation f.

Keywords: Subadditive ergodic theory; Random convex functions; Vector semigroups; 37A30; 37A50 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10959-019-00979-w

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