Monte Carlo Simulation of Reflected Stochastic Differential Equations driven by Poisson Random Measures

2000 ◽  
Vol 6 (1) ◽  
pp. 1-14
Author(s):  
Erika Hausenblas
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Random Measures ◽  
Poisson Random Measures

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.

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