skorokhod representation theorem
Recently Published Documents


TOTAL DOCUMENTS

10
(FIVE YEARS 4)

H-INDEX

4
(FIVE YEARS 0)

2021 ◽  
pp. 495-519
Author(s):  
James Davidson

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.



Author(s):  
Mouhamadou Sy ◽  
Xueying Yu

AbstractIn this paper, our discussion mainly focuses on equations with energy supercritical nonlinearities. We establish probabilistic global well-posedness (GWP) results for the cubic Schrödinger equation with any fractional power of the Laplacian in all dimensions. We consider both low and high regularities in the radial setting, in dimension $$\ge 2$$ ≥ 2 . In the high regularity result, an Inviscid - Infinite dimensional (IID) limit is employed while in the low regularity global well-posedness result, we make use of the Skorokhod representation theorem. The IID limit is presented in details as an independent approach that applies to a wide range of Hamiltonian PDEs. Moreover we discuss the adaptation to the periodic settings, in any dimension, for smooth regularities.



2021 ◽  
pp. 2150046
Author(s):  
Theodore Tachim Medjo ◽  
Caidi Zhao

In this paper, we are interested in proving the existence of a weak martingale solution of the stochastic smectic-A liquid crystal system driven by a pure jump noise in both 2D and 3D bounded domains. We prove the existence of a global weak martingale solution under some non-Lipschitz assumptions on the coefficients. The construction of the solution is based on a Faedo–Galerkin approximation, a compactness method and the Skorokhod representation theorem. In the two-dimensional case, we prove the pathwise uniqueness of the weak solution, which implies the existence of a unique probabilistic strong solution.



2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
T. Tachim Medjo

<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>









1972 ◽  
Vol 4 (2) ◽  
pp. 357-381 ◽  
Author(s):  
Douglas P. Kennedy

Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in the GI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.



1972 ◽  
Vol 4 (02) ◽  
pp. 357-381 ◽  
Author(s):  
Douglas P. Kennedy

Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in theGI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.



Sign in / Sign up

Export Citation Format

Share Document