The topology of information on the space of probability measures over Polish spaces

被引：10

作者：

Barbie, Martin ^{[1
]}

Gupta, Abhishek ^{[2
]}

机构：

[1] Univ Cologne, Ctr Macroecon Res, Cologne, Germany

[2] Univ Illinois, Dept Aerosp Engn, Urbana, IL 61801 USA

来源：

JOURNAL OF MATHEMATICAL ECONOMICS | 2014年 / 52卷

关键词：

Convergence of measures; Topology of information; Conditional independence; Optimization under uncertainty; Games with incomplete information; CONVERGENCE; STRATEGIES; EQUILIBRIA; AGENTS;

D O I：

10.1016/j.jmateco.2014.04.003

中图分类号：

F [经济];

学科分类号：

02 ;

摘要：

We study here the topology of information on the space of probability measures over Polish spaces that was defined in Hellwig (1996). We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence property converges to a measure that also satisfies the same conditional independence property. This also corrects the proof of a claim in Hellwig (1996, Lemma 4). Additionally, we determine sufficient conditions on the Polish spaces and the topology over measure spaces under which a convergent sequence of probability measures is also convergent in the topology of information. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：98 / 111

页数：14

共 8 条

[1] Metrizability of the Levy topology on the space of nonadditive measures on metric spaces
Kawabe, Jun
FUZZY SETS AND SYSTEMS, 2012, 204 : 93 - 105
[2] Infinite convolutions of probability measures on Polish semigroups
Yano, Kouji
PROBABILITY SURVEYS, 2022, 19 : 129 - 159
[3] Sets of Probability Measures and Convex Combination Spaces
Alonso de la Fuente, Miriam
Teran, Pedro
INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITY: THEORIES AND APPLICATIONS, VOL 215, 2023, 215 : 3 - 10
[4] THE DIRICHLET-FERGUSON DIFFUSION ON THE SPACE OF PROBABILITY MEASURES OVER A CLOSED RIEMANNIAN MANIFOLD
Dello Schiavo, Lorenzo
ANNALS OF PROBABILITY, 2022, 50 (02): : 591 - 648
[5] Interpreting systems of continuity equations in spaces of probability measures through PDE duality
Carrillo, Jose A.
Gomez-Castro, David
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2024, 118 (03)
[6] Minimizing Convex Functionals over Space of Probability Measures via KL Divergence Gradient Flow
Yao, Rentian
Huang, Linjun
Yang, Yun
INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS, VOL 238, 2024, 238
[7] NETWORK CONSENSUS IN THE WASSERSTEIN METRIC SPACE OF PROBABILITY MEASURES
Bishop, Adrian N.
Doucet, Arnaud
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2021, 59 (05) : 3261 - 3277
[8] Carathéodory theory and a priori estimates for continuity inclusions in the space of probability measures
Bonnet-Weill, Benoit
Frankowska, Helene
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2024, 247

← 1 →