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The Feynman-Kac formula implies that every suitable classical solution of a semilinear Kolmogorov partial differential equation (PDE) is also a solution of a certain stochastic fixed point equation (SFPE).
Semilinear evolution equations in Banach spaces
Weissler, F. B · 1908
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Non-linear semi-groups
Segal, I · 1963
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Lectures on topics in stochastic differential equations
Stroock, D. W · 1982
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Semigroups of linear operators and applications to partial differential equations
Pazy, A · 1983
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Real and complex analysis
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Brownian motion and stochastic calculus
Karatzas, I., and Shreve, S. E · 1991
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Recursive valuation of defaultable securities and the timing of resolution of uncertainty
Duffie, D., Schroder, M., and Skiadas, C · 1996
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Existence of strong solutions for Itô’s stochastic equations via approximations
Gyöngy, I., and Krylov, N · 1996
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Fundamentals of differential geometry
Lang, S · 1999
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Foundations of modern probability
Kallenberg, O · 2002
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Partial differential equation representations of derivatives with bilateral counterparty risk and funding costs
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Multilevel Picard iterations for solving smooth semilinear parabolic heat equations
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Hutzenthaler, M., and Kruse, T · 2017
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Grohs, P., Hornung, F., Jentzen, A., and Von Wurstemberger, P · 2018
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Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T. A., and von Wurstemberger, P · 2018
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Stochastic partial differential equations: an introduction
Liu, W., and Röckner, M · 2015
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Overcoming the curse of dimensionality in the numerical approximation of Allen–Cahn partial differential equations via truncated full-history recursive multilevel Picard approximations
Beck, C., Hornung, F., Hutzenthaler, M., Jentzen, A., and Kruse, T · 2019
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On multilevel Picard numerical approximations for high-dimensional nonlinear parabolic partial differential equations and high-dimensional nonlinear backward stochastic differential equations
E, W., Hutzenthaler, M., Jentzen, A., and Kruse, T · 2019
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