dissertation_work/Dissertation/main.bbl

\begin{thebibliography}{}

\bibitem[Bass, 2011]{bass_2011}
Bass, R.~F. (2011).
\newblock {\em Brownian Motion}, page 6–12.
\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[Beck et~al., 2021c]{bhj20}
Beck, C., Hutzenthaler, M., and Jentzen, A. (2021c).
\newblock On nonlinear feynman–kac formulas for viscosity solutions of
  semilinear parabolic partial differential equations.
\newblock {\em Stochastics and Dynamics}, 21(08):2150048.

\bibitem[Crandall et~al., 1992]{crandall_lions}
Crandall, M.~G., Ishii, H., and Lions, P.-L. (1992).
\newblock User’s guide to viscosity solutions of second order partial
  differential equations.
\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
  Press.

\bibitem[Durrett, 2019]{durrett2019probability}
Durrett, R. (2019).
\newblock {\em Probability: Theory and Examples}.
\newblock Cambridge Series in Statistical and Probabilistic Mathematics.
  Cambridge University Press.

\bibitem[Golub and Van~Loan, 2013]{golub2013matrix}
Golub, G. and Van~Loan, C. (2013).
\newblock {\em Matrix Computations}.
\newblock Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins
  University Press.

\bibitem[Grohs et~al., 2018]{grohsetal}
Grohs, P., Hornung, F., Jentzen, A., and von Wurstemberger, P. (2018).
\newblock {A proof that artificial neural networks overcome the curse of
  dimensionality in the numerical approximation of Black-Scholes partial
  differential equations}.
\newblock Papers 1809.02362, arXiv.org.

\bibitem[Grohs et~al., 2023]{grohs2019spacetime}
Grohs, P., Hornung, F., Jentzen, A., and Zimmermann, P. (2023).
\newblock Space-time error estimates for deep neural network approximations for
  differential equations.
\newblock {\em Advances in Computational Mathematics}, 49(1):4.

\bibitem[Grohs et~al., 2022]{Grohs_2022}
Grohs, P., Jentzen, A., and Salimova, D. (2022).
\newblock Deep neural network approximations for solutions of {PDEs} based on
  monte carlo algorithms.
\newblock {\em Partial Differential Equations and Applications}, 3(4).

\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., Anh~Nguyen, T., and von
  Wurstemberger, P. (2020a).
\newblock Overcoming the curse of dimensionality in the numerical approximation
  of semilinear parabolic partial differential equations.
\newblock {\em Proceedings of the Royal Society A: Mathematical, Physical and
  Engineering Sciences}, 476(2244):20190630.

\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~Wurstemberger (2020b).
\newblock {Overcoming the curse of dimensionality in the approximative pricing
  of financial derivatives with default risks}.
\newblock {\em Electronic Journal of Probability}, 25(none):1 -- 73.

\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}
Karatzas, I. and Shreve, S. (1991).
\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}