Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Welti, Timo"'
Autor:
Jentzen, Arnulf, Welti, Timo
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce useful result
Externí odkaz:
http://arxiv.org/abs/2003.01291
Autor:
Jentzen, Arnulf, Welti, Timo
Publikováno v:
In Applied Mathematics and Computation 15 October 2023 455
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numerical approximation schemes studied in the scientific literature suffer
Externí odkaz:
http://arxiv.org/abs/1911.03188
Publikováno v:
Eur. J. Appl. Math 32 (2021) 470-514
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number
Externí odkaz:
http://arxiv.org/abs/1908.01602
Publikováno v:
Commun. Math. Sci. 19 (2021), no. 5, 1167-1205
In recent years deep artificial neural networks (DNNs) have been successfully employed in numerical simulations for a multitude of computational problems including, for example, object and face recognition, natural language processing, fraud detectio
Externí odkaz:
http://arxiv.org/abs/1809.07321
Publikováno v:
J. Math. Anal. Appl. 469 (2019), no. 2, 661-704
In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the stochastic B
Externí odkaz:
http://arxiv.org/abs/1710.07123
Publikováno v:
Springer Proc. Math. Stat., 229, Springer, Cham, 2018
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution processes are typically not explicitly known and numerical approximation
Externí odkaz:
http://arxiv.org/abs/1701.04351
Publikováno v:
Nonlinear Anal. 162 (2017), 128-161
In this article we study the differentiability of solutions of parabolic semilinear stochastic evolution equations (SEEs) with respect to their initial values. We prove that if the nonlinear drift coefficients and the nonlinear diffusion coefficients
Externí odkaz:
http://arxiv.org/abs/1611.00856
Publikováno v:
IMA Journal of Numerical Analysis 41, no. 1 (2021): 493-548
We show that if a sequence of piecewise affine linear processes converges in the strong sense with a positive rate to a stochastic process which is strongly H\"older continuous in time, then this sequence converges in the strong sense even with respe
Externí odkaz:
http://arxiv.org/abs/1605.00856
Publikováno v:
Applied Mathematics & Optimization (2021), 1-31
Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved exp
Externí odkaz:
http://arxiv.org/abs/1508.05168