scholarly journals Penalization methods for the Skorokhod problem and reflecting SDEs with jumps

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1750-1775 ◽  
Author(s):  
Weronika Łaukajtys ◽  
Leszek Słomiński
Keyword(s):  
Skorokhod Problem ◽  
Penalization Methods

On a Skorokhod problem with small double limit

2019 ◽  
Vol 30 (5-6) ◽  
pp. 959-972
Author(s):  
Alioune Coulibaly ◽  
Alassane Diedhiou ◽  
Ibrahima Sane
Keyword(s):  
Skorokhod Problem ◽  
Double Limit

scholarly journals Entropy penalization methods for Hamilton–Jacobi equations

2007 ◽  
Vol 215 (1) ◽  
pp. 94-152 ◽  
Author(s):  
Diogo A. Gomes ◽  
Enrico Valdinoci
Keyword(s):  
Penalization Methods ◽  
Jacobi Equations

scholarly journals On the Generalized Drift Skorokhod Problem in One Dimension

2013 ◽  
Vol 50 (1) ◽  
pp. 16-28 ◽  
Author(s):  
Josh Reed ◽  
Amy Ward ◽  
Dongyuan Zhan
Keyword(s):  
Integral Equation ◽  
Time Distribution ◽  
Heavy Traffic ◽  
Hitting Time ◽  
One Dimension ◽  
First Hitting Time ◽  
Skorokhod Problem ◽  
Transient Distribution

We show how to write the solution to the generalized drift Skorokhod problem in one-dimension in terms of the supremum of the solution of a tractable unrestricted integral equation (that is, an integral equation with no boundaries). As an application of our result, we equate the transient distribution of a reflected Ornstein–Uhlenbeck (OU) process to the first hitting time distribution of an OU process (that is not reflected). Then, we use this relationship to approximate the transient distribution of the GI/GI/1 + GI queue in conventional heavy traffic and the M/M/N/N queue in a many-server heavy traffic regime.

scholarly journals State-Constrained Optimization of PDEs via Infinite Penalization Methods

PAMM ◽  
2012 ◽  
Vol 12 (1) ◽  
pp. 691-692
Author(s):  
Richard Barnard ◽  
Martin Frank ◽  
Michael Herty
Keyword(s):  
Constrained Optimization ◽  
Penalization Methods

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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