Vector-valued ergodic theorems for multiparameter Additive processes II

Ryotaro Sato. "Vector-valued ergodic theorems for multiparameter Additive processes II." Colloquium Mathematicae 97.1 (2003): 117-129. <http://eudml.org/doc/284516>.

@article{RyotaroSato2003,
abstract = {Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function $W(·) = ess sup\{||F(I)(·)||: I ⊂ [0, 1)^\{d\}\}$ is integrable on Ω.},
author = {Ryotaro Sato},
journal = {Colloquium Mathematicae},
keywords = {vector-valued additive process; reflexive Banach space; stochastic and pointwise ergodic theorems; -parameter semigroup of linear contractions; contraction majorant},
language = {eng},
number = {1},
pages = {117-129},
title = {Vector-valued ergodic theorems for multiparameter Additive processes II},
url = {http://eudml.org/doc/284516},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Ryotaro Sato
TI - Vector-valued ergodic theorems for multiparameter Additive processes II
JO - Colloquium Mathematicae
PY - 2003
VL - 97
IS - 1
SP - 117
EP - 129
AB - Previously we obtained stochastic and pointwise ergodic theorems for a continuous d-parameter additive process F in L₁((Ω,Σ,μ);X), where X is a reflexive Banach space, under the condition that F is bounded. In this paper we improve the previous results by considering the weaker condition that the function $W(·) = ess sup{||F(I)(·)||: I ⊂ [0, 1)^{d}}$ is integrable on Ω.
LA - eng
KW - vector-valued additive process; reflexive Banach space; stochastic and pointwise ergodic theorems; -parameter semigroup of linear contractions; contraction majorant
UR - http://eudml.org/doc/284516
ER -