EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues ESAIM: M2AN, 36 1 (2002) 33-54 Article references

Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Precise error bounds for numerical approximations of fractional HJB equations

Indranil Chowdhury and Espen R Jakobsen
IMA Journal of Numerical Analysis 45 (2) 633 (2025)
https://doi.org/10.1093/imanum/drae030

Error estimates for the robust α-stable central limit theorem under sublinear expectation by a discrete approximation method

Lianzi Jiang
Journal of Mathematical Analysis and Applications 543 (2) 129028 (2025)
https://doi.org/10.1016/j.jmaa.2024.129028

A Robust $$\alpha $$-Stable Central Limit Theorem Under Sublinear Expectation without Integrability Condition

Lianzi Jiang and Gechun Liang
Journal of Theoretical Probability 37 (3) 2394 (2024)
https://doi.org/10.1007/s10959-023-01298-x

On the rate of convergence for an α-stable central limit theorem under sublinear expectation

Mingshang Hu, Lianzi Jiang and Gechun Liang
Journal of Applied Probability 1 (2024)
https://doi.org/10.1017/jpr.2024.62

A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem

Shuo Huang and Gechun Liang
Journal of Differential Equations 398 1 (2024)
https://doi.org/10.1016/j.jde.2024.03.013

Optimal stability results and nonlinear duality for L∞ entropy and L1 viscosity solutions

Nathaël Alibaud, Jørgen Endal and Espen R. Jakobsen
Journal de Mathématiques Pures et Appliquées 188 26 (2024)
https://doi.org/10.1016/j.matpur.2024.05.003

Continuity of cost in Borkar control topology and implications on discrete space and time approximations for controlled diffusions under several criteria

Somnath Pradhan and Serdar Yüksel
Electronic Journal of Probability 29 (none) (2024)
https://doi.org/10.1214/24-EJP1093

Joint calibration of local volatility models with stochastic interest rates using semimartingale optimal transport

Benjamin Joseph, Grégoire Loeper and Jan Obłój
Quantitative Finance 24 (11) 1597 (2024)
https://doi.org/10.1080/14697688.2024.2398605

Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces

Daria Ghilli and Claudio Marchi
Journal of Mathematical Analysis and Applications 526 (1) 127225 (2023)
https://doi.org/10.1016/j.jmaa.2023.127225

Approximate Q Learning for Controlled Diffusion Processes and Its Near Optimality

Erhan Bayraktar and Ali Devran Kara
SIAM Journal on Mathematics of Data Science 5 (3) 615 (2023)
https://doi.org/10.1137/22M1484201

Stochastic viscosity approximations of Hamilton–Jacobi equations and variance reduction

Grégoire Ferré
ESAIM: Mathematical Modelling and Numerical Analysis 57 (4) 2301 (2023)
https://doi.org/10.1051/m2an/2023042

A universal robust limit theorem for nonlinear Lévy processes under sublinear expectation

Mingshang Hu, Lianzi Jiang, Gechun Liang and Shige Peng
Probability, Uncertainty and Quantitative Risk 1 (2023)
https://doi.org/10.3934/puqr.2023001

Linear Convergence of a Policy Gradient Method for Some Finite Horizon Continuous Time Control Problems

Christoph Reisinger, Wolfgang Stockinger and Yufei Zhang
SIAM Journal on Control and Optimization 61 (6) 3526 (2023)
https://doi.org/10.1137/22M1492180

On representation formulas for optimal control: A Lagrangian perspective

Yeoneung Kim and Insoon Yang
IET Control Theory & Applications 16 (16) 1633 (2022)
https://doi.org/10.1049/cth2.12329

SIR Epidemics with State-Dependent Costs and ICU Constraints: A Hamilton–Jacobi Verification Argument and Dual LP Algorithms

Lorenzo Freddi, Dan Goreac, Juan Li and Boxiang Xu
Applied Mathematics & Optimization 86 (2) (2022)
https://doi.org/10.1007/s00245-022-09884-x

Discrete‐time approximation for stochastic optimal control problems under the G‐expectation framework

Lianzi Jiang
Optimal Control Applications and Methods 43 (2) 418 (2022)
https://doi.org/10.1002/oca.2814

Large-time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN

Guy Barles, Alexander Quaas and Andrei Rodríguez-Paredes
Communications in Partial Differential Equations 46 (3) 547 (2021)
https://doi.org/10.1080/03605302.2020.1846561

Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks

Mo Zhou, Jiequn Han and Jianfeng Lu
SIAM Journal on Scientific Computing 43 (6) A4043 (2021)
https://doi.org/10.1137/21M1402303

Error estimation for second‐order partial differential equations in nonvariational form

Jan Blechschmidt, Roland Herzog and Max Winkler
Numerical Methods for Partial Differential Equations 37 (3) 2190 (2021)
https://doi.org/10.1002/num.22678

Error Estimates for Numerical Approximation of Hamilton–Jacobi Equations Related to Hybrid Control Systems

R. Ferretti, A. Sassi and H. Zidani
Applied Mathematics & Optimization 83 (1) 139 (2021)
https://doi.org/10.1007/s00245-018-9515-8

Some regularity and convergence results for parabolic Hamilton-Jacobi-Bellman equations in bounded domains

Athena Picarelli, Christoph Reisinger and Julen Rotaetxe Arto
Journal of Differential Equations 268 (12) 7843 (2020)
https://doi.org/10.1016/j.jde.2019.11.081

Duality-based a posteriori error estimates for some approximation schemes for optimal investment problems

Athena Picarelli and Christoph Reisinger
Computers & Mathematics with Applications 79 (7) 2099 (2020)
https://doi.org/10.1016/j.camwa.2019.12.010

Approximation schemes for viscosity solutions of fully nonlinear stochastic partial differential equations

Benjamin Seeger
The Annals of Applied Probability 30 (4) (2020)
https://doi.org/10.1214/19-AAP1543

On the Root Solution to the Skorokhod Embedding Problem Given Full Marginals

Alexandre Richard, Xiaolu Tan and Nizar Touzi
SIAM Journal on Control and Optimization 58 (4) 1874 (2020)
https://doi.org/10.1137/18M1222594

Hamilton–Jacobi equations for optimal control on multidimensional junctions with entry costs

Manh-Khang Dao and Boualem Djehiche
Nonlinear Differential Equations and Applications NoDEA 27 (2) (2020)
https://doi.org/10.1007/s00030-020-0625-z

An Approximation Scheme for Semilinear Parabolic PDEs with Convex and Coercive Hamiltonians

Shuo Huang, Gechun Liang and Thaleia Zariphopoulou
SIAM Journal on Control and Optimization 58 (1) 165 (2020)
https://doi.org/10.1137/18M1198831

Error Estimates of Penalty Schemes for Quasi-Variational Inequalities Arising from Impulse Control Problems

Christoph Reisinger and Yufei Zhang
SIAM Journal on Control and Optimization 58 (1) 243 (2020)
https://doi.org/10.1137/19M124040X

Convergence Rate Estimates for Aleksandrov's Solution to the Monge--Ampère Equation

Haodi Chen, Genggeng Huang and Xu-Jia Wang
SIAM Journal on Numerical Analysis 57 (1) 173 (2019)
https://doi.org/10.1137/18M1197217

Probability and Analysis in Interacting Physical Systems

G. T. Kossioris, M. Loulakis and P. E. Souganidis
Springer Proceedings in Mathematics & Statistics, Probability and Analysis in Interacting Physical Systems 283 49 (2019)
https://doi.org/10.1007/978-3-030-15338-0_3

On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations

Imran H. Biswas, Indranil Chowdhury and Espen R. Jakobsen
SIAM Journal on Numerical Analysis 57 (2) 799 (2019)
https://doi.org/10.1137/17M114995X

Improved order 1/4 convergence for piecewise constant policy approximation of stochastic control problems

Espen R. Jakobsen, Athena Picarelli and Christoph Reisinger
Electronic Communications in Probability 24 (none) (2019)
https://doi.org/10.1214/19-ECP256

An analytical solution for the HJB equation arising from the Merton problem

Song-Ping Zhu and Guiyuan Ma
International Journal of Financial Engineering 05 (01) 1850008 (2018)
https://doi.org/10.1142/S2424786318500081

On the structure of multifactor optimal portfolio strategies

Nikolai Dokuchaev
ESAIM: Control, Optimisation and Calculus of Variations 24 (3) 1043 (2018)
https://doi.org/10.1051/cocv/2017013

High-order filtered schemes for time-dependent second order HJB equations

Olivier Bokanowski, Athena Picarelli and Christoph Reisinger
ESAIM: Mathematical Modelling and Numerical Analysis 52 (1) 69 (2018)
https://doi.org/10.1051/m2an/2017039

Convergence of Implicit Schemes for Hamilton--Jacobi--Bellman Quasi-Variational Inequalities

Parsiad Azimzadeh, Erhan Bayraktar and George Labahn
SIAM Journal on Control and Optimization 56 (6) 3994 (2018)
https://doi.org/10.1137/18M1171965

Convergence Rate of an Explicit Finite Difference Scheme for a Credit Rating Migration Problem

Yan Li, Zhengce Zhang and Bei Hu
SIAM Journal on Numerical Analysis 56 (4) 2430 (2018)
https://doi.org/10.1137/17M1151833

Abel-type Results for Controlled Piecewise Deterministic Markov Processes

Dan Goreac and Oana-Silvia Serea
Differential Equations and Dynamical Systems 25 (1) 83 (2017)
https://doi.org/10.1007/s12591-015-0245-y

Qualitative properties of generalized principal eigenvalues for superquadratic viscous Hamilton–Jacobi equations

Emmanuel Chasseigne and Naoyuki Ichihara
Nonlinear Differential Equations and Applications NoDEA 23 (6) (2016)
https://doi.org/10.1007/s00030-016-0422-x

Stochastic Target Games and Dynamic Programming via Regularized Viscosity Solutions

Bruno Bouchard and Marcel Nutz
Mathematics of Operations Research 41 (1) 109 (2016)
https://doi.org/10.1287/moor.2015.0718

A Piecewise Deterministic Markov Toy Model for Traffic/Maintenance and Associated Hamilton–Jacobi Integrodifferential Systems on Networks

Dan Goreac, Magdalena Kobylanski and Miguel Martinez
Applied Mathematics & Optimization 74 (2) 375 (2016)
https://doi.org/10.1007/s00245-015-9319-z

Error estimates for approximations of nonlinear uniformly parabolic equations

Olga Turanova
Nonlinear Differential Equations and Applications NoDEA 22 (3) 345 (2015)
https://doi.org/10.1007/s00030-014-0286-x

(Almost) Everything you always wanted to know about deterministic control problems in stratified domains

Guy Barles and Emmanuel Chasseigne
Networks & Heterogeneous Media 10 (4) 809 (2015)
https://doi.org/10.3934/nhm.2015.10.809

Error estimates for second order Hamilton-Jacobi-Bellman equations. Approximation of probabilistic reachable sets

Mohamed Assellaou, Olivier Bokanowski and Hasnaa Zidani
Discrete & Continuous Dynamical Systems - A 35 (9) 3933 (2015)
https://doi.org/10.3934/dcds.2015.35.3933

Asymptotic Control for a Class of Piecewise Deterministic Markov Processes Associated to Temperate Viruses

Dan Goreac
SIAM Journal on Control and Optimization 53 (4) 1860 (2015)
https://doi.org/10.1137/140998913

On the Rate of Convergence of Finite-Difference Approximations for Elliptic Isaacs Equations in Smooth Domains

N. V. Krylov
Communications in Partial Differential Equations 40 (8) 1393 (2015)
https://doi.org/10.1080/03605302.2015.1029074

Error estimates for approximations of nonhomogeneous nonlinear uniformly elliptic equations

Olga Turanova
Calculus of Variations and Partial Differential Equations 54 (3) 2939 (2015)
https://doi.org/10.1007/s00526-015-0890-6

Extraction of Quantifiable Information from Complex Systems

Jochen Garcke and Irene Klompmaker
Lecture Notes in Computational Science and Engineering, Extraction of Quantifiable Information from Complex Systems 102 179 (2014)
https://doi.org/10.1007/978-3-319-08159-5_9

Existence of Asymptotic Values for Nonexpansive Stochastic Control Systems

Rainer Buckdahn, Dan Goreac and Marc Quincampoix
Applied Mathematics & Optimization 70 (1) 1 (2014)
https://doi.org/10.1007/s00245-013-9230-4

On the Rate of Convergence of Difference Approximations for Uniformly Nondegenerate Elliptic Bellman’s Equations

N. V. Krylov
Applied Mathematics & Optimization 69 (3) 431 (2014)
https://doi.org/10.1007/s00245-013-9228-y

Optimal Production Control of Hybrid Manufacturing/Remanufacturing Failure-Prone Systems under Diffusion-Type Demand

Samir Ouaret, Vladimir Polotski, Jean-Pierre Kenné and Ali Gharbi
Applied Mathematics 04 (03) 550 (2013)
https://doi.org/10.4236/am.2013.43079

A Bellman approach for two-domains optimal control problems in ℝN

G. Barles, A. Briani and E. Chasseigne
ESAIM: Control, Optimisation and Calculus of Variations 19 (3) 710 (2013)
https://doi.org/10.1051/cocv/2012030

Convergence of a semi-discretization scheme for the Hamilton–Jacobi equation: A new approach with the adjoint method

F. Cagnetti, D. Gomes and H.V. Tran
Applied Numerical Mathematics 73 2 (2013)
https://doi.org/10.1016/j.apnum.2013.05.004

Recent Developments in Numerical Methods for Fully Nonlinear Second Order Partial Differential Equations

Xiaobing Feng, Roland Glowinski and Michael Neilan
SIAM Review 55 (2) 205 (2013)
https://doi.org/10.1137/110825960

Linearization Techniques for Controlled Piecewise Deterministic Markov Processes; Application to Zubov’s Method

Dan Goreac and Oana-Silvia Serea
Applied Mathematics & Optimization 66 (2) 209 (2012)
https://doi.org/10.1007/s00245-012-9169-x

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

Dan Goreac
ESAIM: Control, Optimisation and Calculus of Variations 18 (2) 401 (2012)
https://doi.org/10.1051/cocv/2010103

Linearization techniques for $\mathbb{L}^{\infty}$-control problems and dynamic programming principles in classical and $\mathbb{L}^{\infty}$-control problems

Dan Goreac and Oana-Silvia Serea
ESAIM: Control, Optimisation and Calculus of Variations 18 (3) 836 (2012)
https://doi.org/10.1051/cocv/2011183

Some Applications of Linear Programming Formulations in Stochastic Control

Dan Goreac and Oana-Silvia Serea
Journal of Optimization Theory and Applications 155 (2) 572 (2012)
https://doi.org/10.1007/s10957-012-0080-z

Outperforming the market portfolio with a given probability

Erhan Bayraktar, Yu-Jui Huang and Qingshuo Song
The Annals of Applied Probability 22 (4) (2012)
https://doi.org/10.1214/11-AAP799

Subsolutions That Are Close in the Uniform Norm Are Close in the Sobolev Norm as Well

Muhammad Shoaib Saleem and Malkhaz Shashiashvili
Applied Mathematics & Optimization 66 (1) 1 (2012)
https://doi.org/10.1007/s00245-012-9161-5

Penalty Methods for the Solution of Discrete HJB Equations—Continuous Control and Obstacle Problems

J. H. Witte and C. Reisinger
SIAM Journal on Numerical Analysis 50 (2) 595 (2012)
https://doi.org/10.1137/110835840

A probabilistic numerical method for fully nonlinear parabolic PDEs

Arash Fahim, Nizar Touzi and Xavier Warin
The Annals of Applied Probability 21 (4) (2011)
https://doi.org/10.1214/10-AAP723

Mayer and optimal stopping stochastic control problems with discontinuous cost

Dan Goreac and Oana-Silvia Serea
Journal of Mathematical Analysis and Applications 380 (1) 327 (2011)
https://doi.org/10.1016/j.jmaa.2011.02.039

A Penalty Method for the Numerical Solution of Hamilton–Jacobi–Bellman (HJB) Equations in Finance

J. H. Witte and C. Reisinger
SIAM Journal on Numerical Analysis 49 (1) 213 (2011)
https://doi.org/10.1137/100797606

On the convergence rate in multiscale homogenization of fully nonlinear elliptic problems

Fabio Camilli and Claudio Marchi
Networks & Heterogeneous Media 6 (1) 61 (2011)
https://doi.org/10.3934/nhm.2011.6.61

Implications of a regime-switching model on natural gas storage valuation and optimal operation

Zhuliang Chen† and Peter A. Forsyth
Quantitative Finance 10 (2) 159 (2010)
https://doi.org/10.1080/14697680802374791

Merton Problem with Taxes: Characterization, Computation, and Approximation

Imen Ben Tahar, H. Mete Soner and Nizar Touzi
SIAM Journal on Financial Mathematics 1 (1) 366 (2010)
https://doi.org/10.1137/080742178

The problem of optimal control with reflection studied through a linear optimization problem stated on occupational measures

Marc Quincampoix and Oana Silvia Serea
Nonlinear Analysis: Theory, Methods & Applications 72 (6) 2803 (2010)
https://doi.org/10.1016/j.na.2009.11.024

Convergence rates of Markov chain approximation methods for controlled diffusions with stopping

Qingshuo Song and Gang George Yin
Journal of Systems Science and Complexity 23 (3) 600 (2010)
https://doi.org/10.1007/s11424-010-0148-5

Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes

Imran H. Biswas, Espen R. Jakobsen and Kenneth H. Karlsen
Applied Mathematics and Optimization 62 (1) 47 (2010)
https://doi.org/10.1007/s00245-009-9095-8

A Finite Element Like Scheme for Integro-Partial Differential Hamilton–Jacobi–Bellman Equations

Fabio Camilli and Espen R. Jakobsen
SIAM Journal on Numerical Analysis 47 (4) 2407 (2009)
https://doi.org/10.1137/080723144

Rates of Convergence of Numerical Methods for Controlled Regime-Switching Diffusions with Stopping Times in the Costs

Q. S. Song and G. Yin
SIAM Journal on Control and Optimization 48 (3) 1831 (2009)
https://doi.org/10.1137/070679843

Continuous dependence results for non-linear Neumann type boundary value problems

Espen R. Jakobsen and Christine A. Georgelin
Journal of Differential Equations 245 (9) 2368 (2008)
https://doi.org/10.1016/j.jde.2008.07.003

Error estimates for approximate solutions to Bellman equations associated with controlled jump-diffusions

Espen R. Jakobsen, Kenneth H. Karlsen and Claudia La Chioma
Numerische Mathematik 110 (2) 221 (2008)
https://doi.org/10.1007/s00211-008-0160-z

On the Rate of Convergence of the Finite-Difference Approximations for Parabolic Bellman Equations with Constant Coefficients

Jun Luo and N. V. Krylov
Applied Mathematics and Optimization 58 (3) 315 (2008)
https://doi.org/10.1007/s00245-008-9037-x

A rate of convergence for monotone finite difference approximations to fully nonlinear, uniformly elliptic PDEs

Luis A. Caffarelli and Panagiotis E. Souganidis
Communications on Pure and Applied Mathematics 61 (1) 1 (2008)
https://doi.org/10.1002/cpa.20208

ERROR ESTIMATES FOR A CLASS OF FINITE DIFFERENCE-QUADRATURE SCHEMES FOR FULLY NONLINEAR DEGENERATE PARABOLIC INTEGRO-PDES

IMRAN H. BISWAS, ESPEN R. JAKOBSEN and KENNETH H. KARLSEN
Journal of Hyperbolic Differential Equations 05 (01) 187 (2008)
https://doi.org/10.1142/S0219891608001416

NUMERICAL SOLUTIONS FOR THE CHERIDITO-SONER-TOUZI SUPER-REPLICATION MODEL UNDER GAMMA CONSTRAINTS

AGNÈS TOURIN
International Journal of Theoretical and Applied Finance 09 (03) 401 (2006)
https://doi.org/10.1142/S0219024906003561