scholarly journals Stationary tempering and the complex quadrature problem

2002 ◽  
Vol 116 (9) ◽  
pp. 3509-3520 ◽  
Author(s):  
Dubravko Sabo ◽  
J. D. Doll ◽  
David L. Freeman
Keyword(s):  
Quadrature Problem

scholarly journals The Euler–Maruyama scheme for SDEs with irregular drift: convergence rates via reduction to a quadrature problem.

2020 ◽  
Author(s):  
Andreas Neuenkirch ◽  
Michaela Szölgyenyi
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Error Analysis ◽  
Strong Convergence ◽  
General Framework ◽  
Additive Noise ◽  
Convergence Rates ◽  
Convergence Order ◽  
Quadrature Problem ◽  
Weighted Quadrature

Abstract We study the strong convergence order of the Euler–Maruyama (EM) scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted quadrature problem for irregular functions of Brownian motion. Assuming Sobolev–Slobodeckij-type regularity of order $\kappa \in (0,1)$ for the nonsmooth part of the drift, our analysis of the quadrature problem yields the convergence order $\min \{3/4,(1+\kappa )/2\}-\epsilon$ for the equidistant EM scheme (for arbitrarily small $\epsilon>0$). The cut-off of the convergence order at $3/4$ can be overcome by using a suitable nonequidistant discretization, which yields the strong convergence order of $(1+\kappa )/2-\epsilon$ for the corresponding EM scheme.

scholarly journals Optimal quadrature problem on Hardy–Sobolev classes

2005 ◽  
Vol 21 (5) ◽  
pp. 722-739 ◽  
Author(s):  
Fang Gensun ◽  
Li Xuehua
Keyword(s):  
Sobolev Classes ◽  
Optimal Quadrature ◽  
Quadrature Problem

scholarly journals A variation of the Tchebicheff quadrature problem

1967 ◽  
Vol 11 (4) ◽  
pp. 535-546 ◽  
Author(s):  
A. Meir ◽  
A. Sharma
Keyword(s):  
Quadrature Problem

Seeking Primary Functions of Complete Differential with Six Variables

2015 ◽  
Vol 713-715 ◽  
pp. 1899-1902
Author(s):  
Yan Ge Huang ◽  
Wu Sheng Wang ◽  
Hua Ying Zhong
Keyword(s):  
Differential Quadrature ◽  
Quadrature Problem

On the basis of quadrature problem of function with two, three, four and five variables, this paper discuss quadrature problem of function with six variables. Firstly, we have expounded the method of differential quadrature problem. Finally, we solve the primary functions of a specific complete differential with six variables.

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