dissertation_work/Dissertation_unzipped/Dissertation.bbl

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\begin{thebibliography}{}
\bibitem[Bass, 2011]{bass_2011}
Bass, R.~F. (2011).
\newblock {\em Brownian motion}, page 612.
\newblock Cambridge Series in Statistical and Probabilistic Mathematics.
Cambridge University Press.
\bibitem[Beck et~al., 2021a]{Beck_2021}
Beck, C., Gonon, L., Hutzenthaler, M., and Jentzen, A. (2021a).
\newblock On existence and uniqueness properties for solutions of stochastic
fixed point equations.
\newblock {\em Discrete \& Continuous Dynamical Systems - B}, 26(9):4927.
\bibitem[Beck et~al., 2021b]{BHJ21}
Beck, C., Hutzenthaler, M., and Jentzen, A. (2021b).
\newblock On nonlinear {Feynman}{\textendash}{Kac} formulas for viscosity
solutions of semilinear parabolic partial differential equations.
\newblock {\em Stochastics and Dynamics}, 21(08).
\bibitem[Crandall et~al., 1992]{crandall_lions}
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\newblock Users guide to viscosity solutions of second order partial
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\newblock {\em Bull. Amer. Math. Soc.}, 27(1):1--67.
\bibitem[Da~Prato and Zabczyk, 2002]{da_prato_zabczyk_2002}
Da~Prato, G. and Zabczyk, J. (2002).
\newblock {\em Second Order Partial Differential Equations in Hilbert Spaces}.
\newblock London Mathematical Society Lecture Note Series. Cambridge University
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\bibitem[Durrett, 2019]{durrett2019probability}
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\newblock {\em Probability: Theory and Examples}.
\newblock Cambridge Series in Statistical and Probabilistic Mathematics.
Cambridge University Press.
\bibitem[Grohs et~al., 2020]{grohsetal}
Grohs, P., Hornung, F., Jentzen, A., and von Wurstemberger, P. (2020).
\newblock A proof that artificial neural networks overcome the curse of
dimensionality in the numerical approximation of {Black}-{Scholes} partial
differential equations.
\bibitem[Gy{\"o}ngy and Krylov, 1996]{Gyngy1996ExistenceOS}
Gy{\"o}ngy, I. and Krylov, N.~V. (1996).
\newblock Existence of strong solutions for {It\^o}'s stochastic equations via
approximations.
\newblock {\em Probability Theory and Related Fields}, 105:143--158.
\bibitem[Hutzenthaler et~al., 2020a]{hutzenthaler_overcoming_2020}
Hutzenthaler, M., Jentzen, A., Kruse, T., Nguyen, T.~A., and von Wurstemberger,
P. (2020a).
\newblock Overcoming the curse of dimensionality in the numerical approximation
of semilinear parabolic partial differential equations.
\newblock {\em Proc. R. Soc. A.}, 476(2244):20190630.
\newblock arXiv:1807.01212 [cs, math].
\bibitem[Hutzenthaler et~al., 2021]{hutzenthaler_strong_2021}
Hutzenthaler, M., Jentzen, A., Kuckuck, B., and Padgett, J.~L. (2021).
\newblock Strong {$L^p$}-error analysis of nonlinear {Monte} {Carlo}
approximations for high-dimensional semilinear partial differential
equations.
\newblock Technical Report arXiv:2110.08297, arXiv.
\newblock arXiv:2110.08297 [cs, math] type: article.
\bibitem[Hutzenthaler et~al., 2020b]{hjw2020}
Hutzenthaler, M., Jentzen, A., and von Wurstemberger, P. (2020b).
\newblock Overcoming the curse of dimensionality in the approximative pricing
of financial derivatives with default risks.
\newblock page 73 p.
\newblock Artwork Size: 73 p. Medium: application/pdf Publisher: ETH Zurich.
\bibitem[It\^o, 1942a]{Ito1942a}
It\^o, K. (1942a).
\newblock Differential equations determining {Markov} processes (original in
{Japanese}).
\newblock {\em Zenkoku Shijo Sugaku Danwakai}, 244(1077):1352--1400.
\bibitem[It\^o, 1942b]{Ito1946}
It\^o, K. (1942b).
\newblock On a stochastic integral equation.
\newblock {\em Proc. Imperial Acad. Tokyo}, 244(1077):1352--1400.
\bibitem[Karatzas and Shreve, 1991]{karatzas1991brownian}
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\newblock {\em Brownian Motion and Stochastic Calculus}.
\newblock Graduate Texts in Mathematics (113) (Book 113). Springer New York.
\bibitem[Rio, 2009]{rio_moment_2009}
Rio, E. (2009).
\newblock Moment {Inequalities} for {Sums} of {Dependent} {Random} {Variables}
under {Projective} {Conditions}.
\newblock {\em J Theor Probab}, 22(1):146--163.
\end{thebibliography}