scholarly journals Numerical methods for Stochastic differential equations: two examples

2018 ◽  
Vol 64 ◽  
pp. 65-77
Author(s):  
Paul-Éric Chaudru de Raynal ◽  
Gilles Pagès ◽  
Clément Rey
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Simulation Method ◽  
Empirical Measure ◽  
Monte Carlo Simulation Method ◽  
Feller Process ◽  
Skorokhod Problem ◽  
Langevin Monte Carlo

The goal of this paper is to present a series of recent contributions arising in numerical probability. First we present a contribution to a recently introduced problem: stochastic differential equations with constraints in law, investigated through various theoretical and numerical viewpoints. Such a problem may appear as an extension of the famous Skorokhod problem. Then a generic method to approximate in a weak way the invariant distribution of an ergodic Feller process by a Langevin Monte Carlo simulation. It is an extension of a method originally developed for diffusions and based on the weighted empirical measure of an Euler scheme with decreasing step. Finally, we mention without details a recent development of a multilevel Langevin Monte Carlo simulation method for this type of problem.

scholarly journals Uncertainty Cost Functions in Climate-Dependent Controllable Loads in Commercial Environments

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2885
Author(s):  
Daniel Losada ◽  
Ameena Al-Sumaiti ◽  
Sergio Rivera
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Simulation Method ◽  
Electricity Sector ◽  
Cost Functions ◽  
Density Estimator ◽  
Monte Carlo Simulation Method ◽  
Commercial Building ◽  
Complementary Method ◽  
The Cost

This article presents the development, simulation and validation of the uncertainty cost functions for a commercial building with climate-dependent controllable loads, located in Florida, USA. For its development, statistical data on the energy consumption of the building in 2016 were used, along with the deployment of kernel density estimator to characterize its probabilistic behavior. For validation of the uncertainty cost functions, the Monte-Carlo simulation method was used to make comparisons between the analytical results and the results obtained by the method. The cost functions found differential errors of less than 1%, compared to the Monte-Carlo simulation method. With this, there is an analytical approach to the uncertainty costs of the building that can be used in the development of optimal energy dispatches, as well as a complementary method for the probabilistic characterization of the stochastic behavior of agents in the electricity sector.

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