scholarly journals Banach weak topology on Hilbert C✻-modules

2021 ◽  
pp. 1309-1317
Author(s):  
Mehrdad Golabi ◽  
Kourosh Nourouzi
Keyword(s):  
Weak Topology

scholarly journals All adapted topologies are equal

2020 ◽  
Vol 178 (3-4) ◽  
pp. 1125-1172
Author(s):  
Julio Backhoff-Veraguas ◽  
Daniel Bartl ◽  
Mathias Beiglböck ◽  
Manu Eder
Keyword(s):  
Stochastic Processes ◽  
Weak Topology ◽  
Equilibrium Problems ◽  
Diffusion Processes ◽  
Temporal Structure ◽  
Wasserstein Distance ◽  
Optimal Stopping Problems ◽  
Reward Functions ◽  
Nested Distance ◽  
The Stability

Abstract A number of researchers have introduced topological structures on the set of laws of stochastic processes. A unifying goal of these authors is to strengthen the usual weak topology in order to adequately capture the temporal structure of stochastic processes. Aldous defines an extended weak topology based on the weak convergence of prediction processes. In the economic literature, Hellwig introduced the information topology to study the stability of equilibrium problems. Bion–Nadal and Talay introduce a version of the Wasserstein distance between the laws of diffusion processes. Pflug and Pichler consider the nested distance (and the weak nested topology) to obtain continuity of stochastic multistage programming problems. These distances can be seen as a symmetrization of Lassalle’s causal transport problem, but there are also further natural ways to derive a topology from causal transport. Our main result is that all of these seemingly independent approaches define the same topology in finite discrete time. Moreover we show that this ‘weak adapted topology’ is characterized as the coarsest topology that guarantees continuity of optimal stopping problems for continuous bounded reward functions.

Compactness in the Weak Topology

1955 ◽  
Vol 28 (3) ◽  
pp. 125 ◽  
Author(s):  
John Wells Brace
Keyword(s):  
Weak Topology

scholarly journals The weak topology on q-convex Banach function spaces

2011 ◽  
Vol 285 (2-3) ◽  
pp. 136-149 ◽  
Author(s):  
L. Agud ◽  
J. M. Calabuig ◽  
E. A. Sánchez Pérez
Keyword(s):  
Weak Topology ◽  
Function Spaces ◽  
Banach Function Spaces

scholarly journals On the weak topology of Banach spaces over non-archimedean fields

2011 ◽  
Vol 158 (9) ◽  
pp. 1131-1135
Author(s):  
Jerzy Ka̧kol ◽  
Wiesław Śliwa
Keyword(s):  
Banach Spaces ◽  
Weak Topology

scholarly journals Strong Feller solutions to SPDE's are strong Feller in the weak topology

2001 ◽  
Vol 148 (2) ◽  
pp. 111-129 ◽  
Author(s):  
Bohdan Maslowski ◽  
Jan Seidler
Keyword(s):  
Weak Topology ◽  
Strong Feller

scholarly journals Convergence in capacity and applications

2010 ◽  
Vol 107 (1) ◽  
pp. 90 ◽  
Author(s):  
Pham Hoang Hiep
Keyword(s):  
Weak Topology ◽  
Convergence In Capacity

In this article we prove that if $u_j, v_j, w\in\mathcal{E}(\Omega)$ such that $u_j,v_j\geq w$, $\forall\ j\geq 1$, and $|u_j-v_j|\to 0$ in $C_n$-capacity, then $\lim_{j\to\infty}h(\varphi_1,\ldots,\varphi_m) [(dd^cu_j)^n-(dd^cv_j)^n]=0$ in the weak-topology of measures for all $\varphi_1,\ldots ,\varphi_m\in{\operatorname{PSH}}\cap L_{\operatorname {loc}}^\infty (\Omega)$, $h\in C(\mathsf{R}^m)$. We shall then use this result to give some applications.

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