Zobrazeno 1 - 10
of 39
pro vyhledávání: '"Kurniawan, Ryan"'
Autor:
Beccari, Matteo, Hutzenthaler, Martin, Jentzen, Arnulf, Kurniawan, Ryan, Lindner, Felix, Salimova, Diyora
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein scheme) are known to diverge strongly and numerically weakly in the case of one-dimensional stochastic ordinary differential equations with superlinearly growi
Externí odkaz:
http://arxiv.org/abs/1903.06066
In the recent years there has been an increased interest in studying regularity properties of the derivatives of stochastic evolution equations (SEEs) with respect to their initial values. In particular, in the scientific literature it has been shown
Externí odkaz:
http://arxiv.org/abs/1703.09198
Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for numerical approximations of
Externí odkaz:
http://arxiv.org/abs/1612.03209
Publikováno v:
Discrete Contin. Dyn. Syst. Ser. B 23 (2018), no. 6, 2217-2243
The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., \& R\"ockner, M., A mild Ito formula for SPDEs, arXiv:1009.3526 (2012), To appear in the Trans.\ Amer.\ Math.\ Soc.] has turned out to be a useful instrument to study solutions
Externí odkaz:
http://arxiv.org/abs/1612.03210
Publikováno v:
Potential Anal. 50 (2019), no. 3, 347-379
In this article we establish regularity properties for solutions of infinite dimensional Kolmogorov equations. We prove that if the nonlinear drift coefficients, the nonlinear diffusion coefficients, and the initial conditions of the considered Kolmo
Externí odkaz:
http://arxiv.org/abs/1611.00858
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:
J. Math. Anal. Appl. 495 (2021), no. 1, Paper No. 124558, 33 pp
In this article we develop a framework for studying parabolic semilinear stochastic evolution equations (SEEs) with singularities in the initial condition and singularities at the initial time of the time-dependent coefficients of the considered SEE.
Externí odkaz:
http://arxiv.org/abs/1512.06899
Autor:
Jentzen, Arnulf, Kurniawan, Ryan
Publikováno v:
Found. Comput. Math. 21 (2021), no. 2, 445-536
Strong convergence rates for time-discrete numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for time-discrete numerical a
Externí odkaz:
http://arxiv.org/abs/1501.03539
Publikováno v:
Ann. Appl. Probab. 29 (2019), no. 2, 653-716
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates f
Externí odkaz:
http://arxiv.org/abs/1408.1108
Publikováno v:
The Annals of Applied Probability, 2019 Apr 01. 29(2), 653-716.
Externí odkaz:
https://www.jstor.org/stable/26581802
