Zobrazeno 1 - 10
of 112
pro vyhledávání: '"Neuenkirch, Andreas"'
Low-discrepancy points (also called Quasi-Monte Carlo points) are deterministically and cleverly chosen point sets in the unit cube, which provide an approximation of the uniform distribution. We explore two methods based on such low-discrepancy poin
Externí odkaz:
http://arxiv.org/abs/2407.07450
In this paper, we investigate a nonlocal traffic flow model based on a scalar conservation law, where a stochastic velocity function is assumed. In addition to the modeling, theoretical properties of the stochastic nonlocal model are provided, also a
Externí odkaz:
http://arxiv.org/abs/2407.02962
The existence of unique solutions is established for rough differential equations (RDEs) with path-dependent coefficients and driven by c\`adl\`ag rough paths. Moreover, it is shown that the associated solution map, also known as It\^o-Lyons map, is
Externí odkaz:
http://arxiv.org/abs/2403.17573
Autor:
Mickel, Annalena, Neuenkirch, Andreas
We study the Euler scheme for scalar non-autonomous stochastic differential equations, whose diffusion coefficient is not globally Lipschitz but a fractional power of a globally Lipschitz function. We analyse the strong error and establish a criterio
Externí odkaz:
http://arxiv.org/abs/2307.11448
Autor:
Mickel, Annalena, Neuenkirch, Andreas
We study the $L^1$-approximation of the log-Heston SDE at the terminal time point by arbitrary methods that use an equidistant discretization of the driving Brownian motion. We show that such methods can achieve at most order $ \min \{ \nu, \tfrac{1}
Externí odkaz:
http://arxiv.org/abs/2212.07252
Autor:
Mickel, Annalena, Neuenkirch, Andreas
We study the $L^1$-approximation of the log-Heston SDE at equidistant time points by Euler-type methods. We establish the convergence order $ 1/2-\epsilon$ for $\epsilon >0$ arbitrarily small, if the Feller index $\nu$ of the underlying CIR process s
Externí odkaz:
http://arxiv.org/abs/2206.03229
Autor:
Mickel, Annalena, Neuenkirch, Andreas
We study the weak convergence order of two Euler-type discretizations of the log-Heston Model where we use symmetrization and absorption, respectively, to prevent the discretization of the underlying CIR process from becoming negative. If the Feller
Externí odkaz:
http://arxiv.org/abs/2106.10926
On the convergence order of the Euler scheme for scalar SDEs with Hölder-type diffusion coefficients
Autor:
Mickel, Annalena, Neuenkirch, Andreas
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 February 2025 542(1)
Publikováno v:
IMA Journal of Numerical Analysis, draa007, 2020
We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted quadrature pro
Externí odkaz:
http://arxiv.org/abs/1904.07784
Publikováno v:
SIAM J. Numer. Anal. 57-1 (2019), pp. 378-403
We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an adaptive step siz
Externí odkaz:
http://arxiv.org/abs/1802.04521