Estimation of Distribution Systems Expected Energy Not Supplied Index by Multi-level Monte Carlo Method

2019 ◽  
Vol 47 (9-10) ◽  
pp. 810-822
Author(s):  
A. S. Nazmul Huda ◽  
Rastko Živanovic
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Distribution Systems ◽  
Estimation Of Distribution ◽  
Multi Level

scholarly journals On the Acceleration of the Multi-Level Monte Carlo Method

2015 ◽  
Vol 52 (2) ◽  
pp. 307-322 ◽  
Author(s):  
Kristian Debrabant ◽  
Andreas Röβler
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Order Of Convergence ◽  
Optimal Order ◽  
Weak Approximation ◽  
Mean Square ◽  
Optimal Order Of Convergence ◽  
Computational Costs ◽  
The Mean ◽  
Multi Level

The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that the modified estimator reduces the computational costs asymptotically by a factor (p / α)2 if weak approximation methods of orders α and p are applied in the case of computational costs growing with the same order as the variances decay.

scholarly journals STRONG CONVERGENCE FOR EULER–MARUYAMA AND MILSTEIN SCHEMES WITH ASYMPTOTIC METHOD

2014 ◽  
Vol 17 (02) ◽  
pp. 1450014 ◽  
Author(s):  
HIDEYUKI TANAKA ◽  
TOSHIHIRO YAMADA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Strong Convergence ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Convergence Results ◽  
Multi Level ◽  
Alpha Beta ◽  
Sabr Model ◽  
Theoretical Results

Motivated by weak convergence results in the paper of Takahashi & Yoshida (2005), we show strong convergence for an accelerated Euler–Maruyama scheme applied to perturbed stochastic differential equations. The Milstein scheme with the same acceleration is also discussed as an extended result. The theoretical results can be applied to analyze the multi-level Monte Carlo method originally developed by M.B. Giles. Several numerical experiments for the stochastic alpha-beta-rho (SABR) model of stochastic volatility are presented in order to confirm the efficiency of the schemes.

Sign in / Sign up

Export Citation Format

Share Document