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Strong convergence rates on the whole probability space for space-time discrete numerical approximation schemes for stochastic Burgers equations
(2019)SAM Research ReportReport -
Exponential moment bounds and strong convergence rates for tamed-truncated numerical approximations of stochastic convolutions
(2019)SAM Research ReportReport -
On the Itô-Alekseev-Gröbner formula for stochastic differential equations
(2019)SAM Research ReportReport -
A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
(2019)SAM Research ReportReport -
Weak convergence rates for temporal numerical approximations of stochastic wave equations with multiplicative noise
(2019)SAM Research ReportReport -
On existence and uniqueness properties for solutions of stochastic fixed point equations
(2019)SAM Research ReportThe 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). In this article we study such and related SFPEs. In particular, the main result of this work proves existence of unique solutions of certain SFPEs in a general setting. As an application of this main result we establish the existence ...Report -
On the strong regularity of degenerate additive noise driven stochastic differential equations with respect to their initial values
(2019)SAM Research ReportReport