Research Interests

Research Interests

$\bullet$ Complex networks and non-standard growth models.
$\bullet$ Stochastic algorithms, numerical analysis and complexity.
$\bullet$ Stochastic analysis.

Selected Publications

Selected Publications of Steffen Dereich

$\bullet$ S. Dereich, C. Mailler, and P. Mörters. Nonextensive condensation in reinforced branching processes. Ann. Appl. Probab., 27(4):2539–2568, 2017.

$\bullet$ S. Dereich, L. Döring, and A. E. Kyprianou. Real self-similar processes started from the origin. Ann. Probab., 45(3):1952–2003, 2017.

$\bullet$ S. Dereich and S. Li. Multilevel Monte Carlo for Lévy-driven {SDE}s: central limit theorems for adaptive Euler schemes. Ann. Appl. Probab., 26(1):136–185, 2016.

$\bullet$ S. Dereich. Preferential attachment with fitness: unfolding the condensate. Electron. J. Probab., 21:no 3, 38 pp., 2016.

$\bullet$ S. Dereich and P. Mörters. Random networks with sublinear preferential attachment: the giant component. Ann. Probab., 41(1):329–384, 2013.

$\bullet$ S. Dereich. Multilevel Monte Carlo algorithms for Lévy-driven {SDE}s with Gaussian correction. Ann. Appl. Probab., 21(1):283–311, 2011.

$\bullet$ S. Dereich. Rough paths analysis of general Banach space-valued Wiener processes. J. Funct. Anal., 258(9):2910–2936, 2010.

$\bullet$ S. Dereich and P. Mörters. Random networks with sublinear preferential attachment: degree evolutions. Electron. J. Probab., 14:no. 43, 1222–1267, 2009.

$\bullet$ F. Aurzada and S. Dereich. Small deviations of general Lévy processes. Ann. Probab., 37(5):2066–2092, 2009.

$\bullet$ S. Ankirchner, S. Dereich, and P. Imkeller. The Shannon information of filtrations and the additional logarithmic utility of insiders. Ann. Probab., 34(2):743–778, 2006.

Current Publications

$\bullet $ Steffen Dereich and Sebastian Kassing. On minimal representations of shallow ReLU networks. arXiv e-prints, August 2021. arXiv:2108.05643.

$\bullet $ Steffen Dereich and Martin Maiwald. Quasi-processes for branching Markov chains. arXiv e-prints, July 2021. arXiv:2107.06654.

$\bullet $ S. Dereich and S. Kassing. Cooling down stochastic differential equations: almost sure convergence. arXiv e-prints, June 2021. arXiv:2106.03510.

$\bullet $ Steffen Dereich and Sebastian Kassing. Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes. arXiv e-prints, February 2021. arXiv:2102.09385.

$\bullet $ Steffen Dereich. General multilevel adaptations for stochastic approximation algorithms II: CLTs. Stochastic Processes and their Applications, 132:226–260, February 2021. doi:10.1016/

$\bullet $ Steffen Dereich and Sebastian Kassing. Central limit theorems for stochastic gradient descent with averaging for stable manifolds. arXiv e-prints, December 2019. arXiv:1912.09187.