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We extend a recently developed method to solve semi-linear PDEs to the case of a degenerated diffusion.
Systems & Control Letters 14
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Finance and Stochastics 3
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Finance and stochastics 5
Zariphopoulou, T.: A solution approach to valuation with unhedgeable risks · 2001
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Stochastic Processes and their applications 111
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The Annals of Applied Probability 15
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Quantitative Finance 6
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Bernoulli 12
Lemor, J.P., Gobet, E., Warin, X., et al.: Rate of convergence of an empirical regression method for solving generalized backward stochastic differential equations · 2006
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Communications on Pure and Applied Mathematics 60
Cheridito, P., Soner, H.M., Touzi, N., Victoir, N.: Second-order backward stochastic differential equations and fully nonlinear parabolic pdes · 2007
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Bauke, H.: Tina’s random number generator library (2011)
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The Annals of Applied Probability pp. 1322–1364 (2011)
Fahim, A., Touzi, N., Warin, X.: A probabilistic numerical method for fully nonlinear parabolic pdes · 2011
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Springer Science & Business Media (2012)
Touzi, N.: Optimal stochastic control, stochastic target problems, and backward SDE, vol. 29 · 2012
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Electronic Journal of Probability 18
Tan, X.: A splitting method for fully nonlinear degenerate parabolic pdes · 2013
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ESAIM: Probability and Statistics 21
Doumbia, M., Oudjane, N., Warin, X.: Unbiased monte carlo estimate of stochastic differential equations expectations · 2017
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Communications in Mathematics and Statistics 5
E, W., Han, J., Jentzen, A.: Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations · 2017
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arXiv preprint arXiv:1707.02568 (2017)
E, W., Han, J., Jentzen, A.: Overcoming the curse of dimensionality: Solving high-dimensional partial differential equations using deep learning · 2017
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SAM Research Report 2017
E, W., Hutzenthaler, M., Jentzen, A., Kruse, T.: Linear scaling algorithms for solving high-dimensional nonlinear parabolic differential equations · 2017
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arXiv preprint arXiv:1711.01080 (2017)
Hutzenthaler, M., Kruse, T.: Multi-level picard approximations of high-dimensional semilinear parabolic differential equations with gradient-dependent nonlinearities · 2017
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E, W., Hutzenthaler, M., Jentzen, A., Kruse, T.: On multilevel picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations · 2016
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arXiv preprint arXiv:1603.01727 (2016)
Henry-Labordere, P., Oudjane, N., Tan, X., Touzi, N., Warin, X.: Branching diffusion representation of semilinear pdes and monte carlo approximation · 2016
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arXiv preprint arXiv:1709.05963 (2017)
Beck, C., E, W., Jentzen, A.: Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations · 2017
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arXiv preprint arXiv:1701.07660 (2017)
Warin, X.: Variations on branching methods for non linear pdes · 2017
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arXiv preprint arXiv:1804.08432 (2018)
Warin, X.: Nesting monte carlo for high-dimensional non linear pdes · 2018
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