Open Mappings of Probability Measures and the Skorokhod Representation Theorem

2002 ◽  
Vol 46 (1) ◽  
pp. 20-38 ◽  
Author(s):  
V. I. Bogachev ◽  
A. V. Kolesnikov
Keyword(s):  
Representation Theorem ◽  
Probability Measures ◽  
Skorokhod Representation Theorem

Weak Convergence of Distributions

2021 ◽  
pp. 495-519
Author(s):  
James Davidson
Keyword(s):  
Weak Convergence ◽  
Representation Theorem ◽  
Stable Distribution ◽  
Characteristic Functions ◽  
Random Sums ◽  
Skorokhod Representation Theorem

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved and the chapter then considers the preservation of weak convergence under transformations. Next, the role of moments and characteristic functions is considered. In the leading case of random sums, the criteria for weak convergence and the concept of a stable distribution are studied.

scholarly journals On weak martingale solutions to a stochastic Allen-Cahn-Navier-Stokes model with inertial effects

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
T. Tachim Medjo
Keyword(s):  
Representation Theorem ◽  
Multiplicative Noise ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Inertial Effects ◽  
Navier Stokes Equations ◽  
Martingale Solution ◽  
Skorokhod Representation Theorem ◽  
Martingale Solutions

<p style='text-indent:20px;'>We consider a stochastic Allen-Cahn-Navier-Stokes equations with inertial effects in a bounded domain <inline-formula><tex-math id="M1">\begin{document}$ D\subset\mathbb{R}^{d} $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ d = 2, 3 $\end{document}</tex-math></inline-formula>, driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non-Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo-Galerkin approximation, compactness method and the Skorokhod representation theorem.</p>

Weak Convergence

2021 ◽  
pp. 638-667
Author(s):  
James Davidson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
Central Limit ◽  
Representation Theorem ◽  
Metric Spaces ◽  
Continuous Functions ◽  
Probability Measures ◽  
Functional Central Limit ◽  
Spaces Of Measures

This chapter reviews the theory of weak convergence in metric spaces. Topics include Skorokhod’s representation theorem, the metrization of spaces of measures, and the concept of tightness of probability measures. The key relation is shown between weak convergence and uniform tightness. Considering the space C of continuous functions in particular, the functional central limit theorem is proved for martingales, together with extensions to the multivariate case.

scholarly journals The Riesz representation theorem and weak∗ compactness of semimartingales

2020 ◽  
Vol 24 (4) ◽  
pp. 827-870
Author(s):  
Matti Kiiski
Keyword(s):  
Representation Theorem ◽  
Continuous Functions ◽  
Weak Compactness ◽  
Probability Measures ◽  
Compact Set ◽  
Riesz Representation Theorem ◽  
Radon Measures ◽  
Riesz Representation ◽  
Sequential Closure ◽  
Bounded Continuous Functions

Abstract We show that the sequential closure of a family of probability measures on the canonical space of càdlàg paths satisfying Stricker’s uniform tightness condition is a weak∗ compact set of semimartingale measures in the dual pairing of bounded continuous functions and Radon measures, that is, the dual pairing from the Riesz representation theorem under topological assumptions on the path space. Similar results are obtained for quasi- and supermartingales under analogous conditions. In particular, we give a full characterisation of the strongest topology on the Skorokhod space for which these results are true.

LIFTING THE FUNCTOR ITO THE CATEGORY OF UNIFORM SPACES

2020 ◽  
Vol 4 (1) ◽  
pp. 29-39
Author(s):  
Dilrabo Eshkobilova ◽  
Keyword(s):  
Compact Support ◽  
Probability Measures ◽  
Uniform Spaces ◽  
Continuous Maps ◽  
Uniformly Continuous

Uniform properties of the functor Iof idempotent probability measures with compact support are studied. It is proved that this functor can be lifted to the category Unif of uniform spaces and uniformly continuous maps

Sign in / Sign up

Export Citation Format

Share Document