On Multivalued Amarts

Dorota Dudek, and Wiesław Zięba. "On Multivalued Amarts." Bulletin of the Polish Academy of Sciences. Mathematics 52.1 (2004): 93-99. <http://eudml.org/doc/280920>.

@article{DorotaDudek2004,
abstract = {In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.},
author = {Dorota Dudek, Wiesław Zięba},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {multivalued martingale; almost sure convergence},
language = {eng},
number = {1},
pages = {93-99},
title = {On Multivalued Amarts},
url = {http://eudml.org/doc/280920},
volume = {52},
year = {2004},
}

TY - JOUR
AU - Dorota Dudek
AU - Wiesław Zięba
TI - On Multivalued Amarts
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2004
VL - 52
IS - 1
SP - 93
EP - 99
AB - In recent years, convergence results for multivalued functions have been developed and used in several areas of applied mathematics: mathematical economics, optimal control, mechanics, etc. The aim of this note is to give a criterion of almost sure convergence for multivalued asymptotic martingales (amarts). For every separable Banach space B the fact that every L¹-bounded B-valued martingale converges a.s. in norm to an integrable B-valued random variable (r.v.) is equivalent to the Radon-Nikodym property [6]. In this paper we solve the problem of a.s. convergence of multivalued amarts by giving a topological characterization.
LA - eng
KW - multivalued martingale; almost sure convergence
UR - http://eudml.org/doc/280920
ER -