Multivariate Monte Carlo Approximation Based on Scattered Data

2020 ◽  
Vol 42 (4) ◽  
pp. A2262-A2280 ◽  
Author(s):  
Wenwu Gao ◽  
Xingping Sun ◽  
Zongmin Wu ◽  
Xuan Zhou
Keyword(s):  
Monte Carlo ◽  
Scattered Data ◽  
Monte Carlo Approximation

scholarly journals Branching diffusion representation of semilinear PDEs and Monte Carlo approximation

2019 ◽  
Vol 55 (1) ◽  
pp. 184-210 ◽  
Author(s):  
Pierre Henry-Labordère ◽  
Nadia Oudjane ◽  
Xiaolu Tan ◽  
Nizar Touzi ◽  
Xavier Warin
Keyword(s):  
Monte Carlo ◽  
Branching Diffusion ◽  
Monte Carlo Approximation ◽  
Semilinear Pdes

Monte carlo approximation to edgeworth expansions

1999 ◽  
Vol 27 (3) ◽  
pp. 579-584
Author(s):  
Peter Hall ◽  
Michael A. Martin ◽  
Shan Sun
Keyword(s):  
Monte Carlo ◽  
Edgeworth Expansions ◽  
Monte Carlo Approximation

scholarly journals Randomized exponential integrators for modulated nonlinear Schrödinger equations

2020 ◽  
Vol 40 (4) ◽  
pp. 2143-2162
Author(s):  
Martina Hofmanová ◽  
Marvin Knöller ◽  
Katharina Schratz
Keyword(s):  
Monte Carlo ◽  
Convergence Rates ◽  
Order Reduction ◽  
Time Dependent ◽  
New Approach ◽  
Nonlinear Schrödinger ◽  
Monte Carlo Approximation ◽  
Exponential Integrator ◽  
Discretization Technique ◽  
Error Behavior

Abstract We consider the nonlinear Schrödinger equation with dispersion modulated by a (formal) derivative of a time-dependent function with fractional Sobolev regularity of class $W^{\alpha ,2}$ for some $\alpha \in (0,1)$. Due to the loss of smoothness in the problem, classical numerical methods face severe order reduction. In this work, we develop and analyze a new randomized exponential integrator based on a stratified Monte Carlo approximation. The new discretization technique averages the high oscillations in the solution allowing for improved convergence rates of order $\alpha +1/2$. In addition, the new approach allows us to treat a far more general class of modulations than the available literature. Numerical results underline our theoretical findings and show the favorable error behavior of our new scheme compared to classical methods.

Monte Carlo Approximation of Bootstrap Variances

1998 ◽  
Vol 52 (4) ◽  
pp. 354 ◽  
Author(s):  
James G. Booth ◽  
Somnath Sarkar
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Approximation
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