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It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs).
NeuroDiffEq: A Python package for solving differential equations with neural networks
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Donsker-type theorem for BSDEs
Briand, P., Delyon, B., and Mémin, J · 2001
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Multilevel Monte Carlo methods
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Ma, J., Protter, P., San Martín, J., and Torres, S · 2002
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Error analysis of the optimal quantization algorithm for obstacle problems
Bally, V., and Pagès, G · 2003
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A quantization algorithm for solving multi-dimensional discrete-time optimal stopping problems
Bally, V., and Pagès, G · 2003
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Numerical solution of elliptic partial differential equation using radial basis function neural networks
Jianyu, L., Siwei, L., Yingjian, Q., and Yaping, H · 2003
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Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations
Bouchard, B., and Touzi, N · 2004
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A regression-based Monte Carlo method to solve backward stochastic differential equations
Gobet, E., Lemor, J.-P., and Warin, X · 2005
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Explicit exponential Runge–Kutta methods for semilinear parabolic problems
Hochbruck, M., and Ostermann, A · 2005
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Delarue, F., and Menozzi, S · 2006
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Numerical simulation of BSDEs using empirical regression methods: theory and practice
Gobet, E., and Lemor, J.-P · 2006
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Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations
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Peskir, G., and Shiryaev, A · 2006
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Bender, C., and Denk, R · 2007
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Time discretization and Markovian iteration for coupled FBSDEs
Bender, C., and Zhang, J · 2008
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An interpolated stochastic algorithm for quasi-linear PDEs
Delarue, F., and Menozzi, S · 2008
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Multilevel Monte Carlo path simulation
Giles, M. B · 2008
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Pathwise numerical approximation of SPDEs with additive noise under non-global Lipschitz coefficients
Jentzen, A · 2009
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Crisan, D., Manolarakis, K., and Touzi, N · 2010
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Glorot, X., and Bengio, Y · 2010
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Gobet, E., and Labart, C · 2010
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Results on numerics for FBSDE with drivers of quadratic growth
Imkeller, P., Dos Reis, G., and Zhang, J · 2010
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A stable multistep scheme for solving backward stochastic differential equations
Zhao, W., Zhang, G., and Ju, L · 2010
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Malliavin calculus for backward stochastic differential equations and application to numerical solutions
Hu, Y., Nualart, D., and Song, X · 2011
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Numerical method for reflected backward stochastic differential equations
Martinez, M., San Martín, J., and Torres, S · 2011
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Least-squares Monte Carlo for backward SDEs
Bender, C., and Steiner, J · 2012
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Solving backward stochastic differential equations using the cubature method: Application to nonlinear pricing
Crisan, D., and Manolarakis, K · 2012
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Henry-Labordère, P · 2012
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Markovian quadratic and superquadratic BSDEs with an unbounded terminal condition
Richou, A · 2012
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BS Δ \Delta Es and BSDEs with non-Lipschitz drivers: comparison, convergence and robustness
Cheridito, P., and Stadje, M · 2013
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Pathwise Hölder convergence of the implicit-linear Euler scheme for semi-linear SPDEs with multiplicative noise
Cox, S., and van Neerven, J · 2013
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A parallel algorithm for solving BSDEs
Labart, C., and Lelong, J · 2013
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Simulation of BSDEs by Wiener chaos expansion
Briand, P., and Labart, C · 2014
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Second order discretization of backward SDEs and simulation with the cubature method
Crisan, D., and Manolarakis, K · 2014
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A numerical algorithm for a class of BSDEs via the branching process
Henry-Labordère, P., Tan, X., and Touzi, N · 2014
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Linear Hamilton Jacobi Bellman equations in high dimensions
Horowitz, M. B., Damle, A., and Burdick, J. W · 2014
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Adam: A method for stochastic optimization
Kingma, D. P., and Ba, J · 2014
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New kinds of high-order multistep schemes for coupled forward backward stochastic differential equations
Zhao, W., Fu, Y., and Zhou, T · 2014
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Numerical stability analysis of the Euler scheme for BSDEs
Chassagneux, J.-F., and Richou, A · 2015
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Clevert, D.-A., Unterthiner, T., and Hochreiter, S · 2015
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A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations
de Raynal, P. C., and Trillos, C. G · 2015
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Multilevel Monte Carlo methods
Giles, M. B · 2015
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Loss of regularity for Kolmogorov equations
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Ioffe, S., and Szegedy, C · 2015
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Multistep schemes for forward backward stochastic differential equations with jumps
Fu, Y., Zhao, W., and Zhou, T · 2016
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Simulation of BSDEs with jumps by Wiener Chaos expansion
Geiss, C., and Labart, C · 2016
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Gobet, E., López-Salas, J. G., Turkedjiev, P., and Vázquez, C · 2016
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Approximation of backward stochastic differential equations using Malliavin weights and least-squares regression
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Linear regression MDP scheme for discrete backward stochastic differential equations under general conditions
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Eigel, M., Pfeffer, M., and Schneider, R · 2017
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Deep Primal-Dual Algorithm for BSDEs: Applications of Machine Learning to CVA and IM
Henry-Labordère, P · 2017
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Le Cavil, A., Oudjane, N., and Russo, F · 2017
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Raissi, M., Perdikaris, P., and Karniadakis, G. E · 2017
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Variations on branching methods for non linear PDEs
Warin, X · 2017
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A unified deep artificial neural network approach to partial differential equations in complex geometries
Berg, J., and Nyström, K · 2018
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Cai, Z., and Liu, J · 2018
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