Numerical resolution of McKean-Vlasov FBSDEs using neural networks.
暂无分享,去创建一个
[1] François Delarue,et al. Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games , 2018 .
[2] Jimmy Ba,et al. Adam: A Method for Stochastic Optimization , 2014, ICLR.
[3] Mathieu Lauriere,et al. Numerical Methods for Mean Field Games and Mean Field Type Control , 2021, Proceedings of Symposia in Applied Mathematics.
[4] E Weinan,et al. Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations , 2017, J. Nonlinear Sci..
[5] Alexander Sergeev,et al. Horovod: fast and easy distributed deep learning in TensorFlow , 2018, ArXiv.
[6] D. Crisan,et al. A Probabilistic Approach to Classical Solutions of the Master Equation for Large Population Equilibria , 2014, Memoirs of the American Mathematical Society.
[7] Xavier Warin,et al. Machine Learning for Semi Linear PDEs , 2018, Journal of Scientific Computing.
[8] B. Bouchard,et al. Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations , 2004 .
[9] Ying Peng,et al. Three Algorithms for Solving High-Dimensional Fully Coupled FBSDEs Through Deep Learning , 2019, IEEE Intelligent Systems.
[10] Jean-Pierre Fouque,et al. Deep Learning Methods for Mean Field Control Problems With Delay , 2019, Frontiers in Applied Mathematics and Statistics.
[11] Jiequn Han,et al. Convergence of the deep BSDE method for coupled FBSDEs , 2018, Probability, Uncertainty and Quantitative Risk.
[12] Mathieu Laurière,et al. Convergence Analysis of Machine Learning Algorithms for the Numerical Solution of Mean Field Control and Games: I - The Ergodic Case , 2019, The Annals of Applied Probability.
[13] Dan Crisan,et al. CLASSICAL SOLUTIONS TO THE MASTER EQUATION FOR LARGE POPULATION EQUILIBRIA , 2014 .
[14] P. Lions,et al. Jeux à champ moyen. II – Horizon fini et contrôle optimal , 2006 .
[15] P. Cardaliaguet,et al. Mean field game of controls and an application to trade crowding , 2016, 1610.09904.
[16] Cem Anil,et al. Sorting out Lipschitz function approximation , 2018, ICML.
[17] Arnulf Jentzen,et al. Solving high-dimensional partial differential equations using deep learning , 2017, Proceedings of the National Academy of Sciences.
[18] E. Gobet,et al. A regression-based Monte Carlo method to solve backward stochastic differential equations , 2005, math/0508491.
[19] Christy V. Graves,et al. Cemracs 2017: numerical probabilistic approach to MFG , 2019, ESAIM: Proceedings and Surveys.
[20] R. Carmona,et al. A probabilistic weak formulation of mean field games and applications , 2013, 1307.1152.
[21] Yves Achdou,et al. Mean Field Games: Numerical Methods , 2010, SIAM J. Numer. Anal..
[22] P. Lions,et al. Jeux à champ moyen. I – Le cas stationnaire , 2006 .
[23] Yuan Yu,et al. TensorFlow: A system for large-scale machine learning , 2016, OSDI.
[24] Dan Crisan,et al. Numerical method for FBSDEs of McKean–Vlasov type , 2017, The Annals of Applied Probability.
[25] Huyên Pham,et al. Deep Neural Networks Algorithms for Stochastic Control Problems on Finite Horizon: Convergence Analysis , 2021, SIAM J. Numer. Anal..
[26] Huyên Pham,et al. Some machine learning schemes for high-dimensional nonlinear PDEs , 2019, ArXiv.
[27] Huyên Pham,et al. Deep backward schemes for high-dimensional nonlinear PDEs , 2019 .
[28] René Carmona,et al. Probabilistic Analysis of Mean-field Games , 2013 .
[29] Huyen Pham,et al. Neural networks-based backward scheme for fully nonlinear PDEs , 2019, SN Partial Differential Equations and Applications.
[30] Arnulf Jentzen,et al. Deep splitting method for parabolic PDEs , 2019, SIAM J. Sci. Comput..