Vector-valued ergodic theorems for multiparameter additive processes

Sato, Ryotaro

Sato, Ryotaro

Colloquium Mathematicae, Tome 79 (1999), p. 193-202 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be a reflexive Banach space and (Ω,Σ,μ) be a σ-finite measure space. Let d ≥ 1 be an integer and T=T(u):u=( $u_{1}$ , ... , $u_{d})$ , $u_{i}$ ≥ 0, 1 ≤ i ≤ d be a strongly measurable d-parameter semigroup of linear contractions on $L_{1}$ ((Ω,Σ,μ);X). We assume that to each T(u) there corresponds a positive linear contraction P(u) defined on $L_{1}$ ((Ω,Σ,μ);ℝ) with the property that ∥ T(u)f(ω)∥ ≤ P(u)∥f(·)∥(ω) almost everywhere on Ω for all f ∈ $L_{1}$ ((Ω,Σ,μ);X). We then prove stochastic and pointwise ergodic theorems for a d-parameter bounded additive process F in $L_{1}$ ((Ω,Σ,μ);X) with respect to the semigroup T.

Publié le : 1999-01-01

Zbl 0947.47005

EUDML-ID : urn:eudml:doc:210634

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     author = {Ryotaro Sato},
     title = {Vector-valued ergodic theorems for multiparameter additive processes},
     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {193-202},
     zbl = {0947.47005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p193bwm}
}

Sato, Ryotaro. Vector-valued ergodic theorems for multiparameter additive processes. Colloquium Mathematicae, Tome 79 (1999) pp. 193-202. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv79z2p193bwm/

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