![]() |
![]() |
ETNA - Electronic Transactions on Numerical Analysis
|
![]() |
Verlag der Österreichischen Akademie der Wissenschaften Austrian Academy of Sciences Press
A-1011 Wien, Dr. Ignaz Seipel-Platz 2
Tel. +43-1-515 81/DW 3420, Fax +43-1-515 81/DW 3400 https://verlag.oeaw.ac.at, e-mail: verlag@oeaw.ac.at |
![]() |
|
DATUM, UNTERSCHRIFT / DATE, SIGNATURE
BANK AUSTRIA CREDITANSTALT, WIEN (IBAN AT04 1100 0006 2280 0100, BIC BKAUATWW), DEUTSCHE BANK MÜNCHEN (IBAN DE16 7007 0024 0238 8270 00, BIC DEUTDEDBMUC)
|
ETNA - Electronic Transactions on Numerical Analysis, pp. 483-498, 2021/07/05
We analyze three iterative methods that have been proposed in the computational physics community for the reconstruction of memory kernels in a stochastic delay differential equation known as the generalized Langevin equation. These methods use the autocorrelation function of the solution of this equation as input data. Although they have been demonstrated to be useful, a straightforward Laplace analysis does not support their conjectured convergence. We provide more detailed arguments to explain the good performance of these methods in practice. In the second part of this paper we investigate the solution of the generalized Langevin equation with a perturbed memory kernel. We establish sufficient conditions including error bounds such that the stochastic process corresponding to the perturbed problem converges to the unperturbed process in the mean square sense.
Keywords: generalized Langevin equation, Laplace transform, strong convergence