scholarly journals On the Skorokhod representation theorem

2007 ◽  
Vol 135 (12) ◽  
pp. 3995-4008 ◽  
Author(s):  
Jean Cortissoz
Keyword(s):  
Representation Theorem ◽  
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>

scholarly journals Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized (h,e)-Implications

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1490
Author(s):  
Raquel Fernandez-Peralta ◽  
Sebastia Massanet ◽  
Arnau Mir
Keyword(s):  
Representation Theorem ◽  
Internal Factors ◽  
Fuzzy Implication ◽  
The Family

In this study, we analyze the family of generalized (h,e)-implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized (h,e)-implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the (f,g) and (g,f)-implications, which are two families of fuzzy implication functions that generalize the well-known f and g-generated implications proposed by Yager through a generalization of the internal factors x and 1x, respectively. The behavior and additional properties of these two families are also studied in detail.

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