Prof. Dr. Steffen Dereich
© Steffen Dereich
Prof. Dr. Steffen Dereich
Room 130.008
Orléans-Ring 10
48149 Münster
T: 0251 83-32671
steffen.dereich@uni-muenster.de
Consultation hours: by arragement

  • Teaching

    SS 2023 Stochastics for Teachers BSc Seminar Stochastik
    WS 2022/23 Mathematical Statistics MSc Seminar on Probability Theory

    SS 2022

    		 Markov Processes MSc Seminar on Probability Theory
    WS 2021/22 Stochastic Analysis MSc Seminar on Probability Theory
    SS 2021 Stochastic Approximation MSc Seminar Stochastic Processes
    WS 2020/21 Stochastic Analysis MSc Seminar on Gaussian processes
    SS 2020 Rough paths and their applications in machine learning BSc Seminar on probability theory
    WS 2019/20 Financial Mathematics BSc Seminar on probability theory
    SS 2019 Probability theory BSc Seminar: Machine Learning and Stochastic Finance
    WS 2018/19 Stochastics Seminar for teachers: Markov chains
    SS 2018 Stochastics for Teachers Seminar for teachers
    SS 2017 Markov Processes MSc Seminar "Stochastic Processes"
    WS 2016/17 Stochastic Analysis MSc Seminar "Stochastic Processes"
    SS 2016 Point Processes BSc Seminar "Monte Carlo algorithms"
    WS 2015/16 Financial Mathematics I BSc Seminar "Markov-chains"
    SS 2015 Probability Theory MSc Seminar "Large Deviations"
    WS 2014/15 Stochastics MSc Seminar "Probability"
    SS 2014 Stochastic Models MSc Seminar "Branching Processes"
    WS 2013/14 Markov Processes MSc Seminar "Complex Networks"
    WS 2012/13 Financial Mathematics I BSc Seminar "Monte Carlo algorithms"
    SS 2012 Probability Theory  
    WS 2011/12 Stochastics  

     

  • Publications

     Preprints

    • Traces left by random walks on large random graphs: local limits
      arXiv:2403.14787
      Preprint

    • On the existence of optimal shallow feedforward networks with ReLU activation
      joint work with Sebastian Kassing
      J. Mach. Learn. 3, No. 1, 1-22 (2024), DOI: 10.4208/jml.230903
      arXiv:2303.03950
      Preprint

    • On the existence of minimizers in shallow residual ReLU neural network optimization landscapes
      joint work with Arnulf Jentzen and Sebastian Kassing
      arXiv:2302.14690
      Preprint
    • Quasi-processes for branching Markov chains
      joint work with Martin Maiwald
      arXiv:2107.06654
      Preprint
    • Convergence of stochastic gradient descent schemes for Lojasiewicz-landscapes
      joint work with Sebastian Kassing
      arXiv:2102.09385
      Preprint

    Artificial neural networks / Stochastic approximation

    • Central limit theorems for stochastic gradient descent with averaging for stable manifolds
      joint work with Sebastian Kassing
      Electron. J. Probab. 28: 1-48 (2023), DOI: 10.1214/23-EJP947
      PDF
    • On minimal representations of shallow ReLU networks
      joint work with Sebastian Kassing
      Neural Networks 148, 121-128 (2022), DOI 10.1016/j.neunet.2022.01.006
      Preprint
    • Cooling down stochastic differential equations: almost sure convergence
      joint work with Sebastian Kassing
      Stochastic Process. Appl. 152, 289-311 (2022), DOI 10.1016/j.spa.2022.06.020
      Preprint
    • General multilevel adaptations for stochastic approximation algorithms II: CLTs
      Stochastic Process. Appl. 132, 226-260 (2021), DOI 10.1016/j.spa.2020.11.001
      Preprint
    • General multilevel adaptations for stochastic approximation algorithms of Robbins-Monro and Polyak-Ruppert type
      joint work with Thomas Müller-Gronbach
      Numer. Math. 142, No. 2, 279-328 (2019), DOI 10.1007/s00211-019-01024-y
      Preprint

    Complex networks / Condensation

    • The rank-one and the preferential attachment paradigm
      In Network Science - An Aerial View, 43-58 (2019)
    • Local neighbourhoods for first passage percolation on the configuration model
      joint work with Marcel Ortgiese
      J. Stat. Phys. 137, No. 3-4, 485-501 (2018), DOI 10.1007/s10955-018-2028-7
      Preprint
    • The shape of the emerging condensate in effective models of condensation
      joint work with Volker Betz and Peter Mörters
      Ann. Henri Poincaré 19, No. 6, 1869-1889 (2018)
      Preprint
    • Non-extensive condensation in reinforced branching processes
      joint work with Cécile Mailler and Peter Mörters
      Ann. Appl. Probab. 27, No. 4, 2539-2568 (2017)
      Preprint
    • Distances in scale free networks at criticality
      joint work with Christian Mönch and Peter Mörters
      Electron. J. Probab. 22, No. 77, 38 pp. (2017)
      PDF
    • Preferential attachment with fitness: unfolding the condensate
      Electron. J. Probab. 21, No. 3, 1-38 (2016)
      PDF
    • Cycle length distributions in random permutations with diverging cycle weights
      joint work with Peter Mörters
      Random. Struct. Algor. 46, No. 4, 635-650 (2015)
      PDF
    • Robust analysis of preferential attachment models with fitness
      joint work with Marcel Ortgiese
      Combin. Probab. Comput. 23, No. 3, 386-411 (2014), DOI 10.1017/S0963548314000157
      Preprint
    • Emergence of condensation in Kingman's model of selection and mutation
      joint work with Peter Mörters
      Acta Appl. Math. 127, No. 1, 17-26 (2013), DOI 10.1007/s10440-012-9790-3 
      Preprint 
    • Typical distances in ultrasmall random networks
      joint work with Christian Mönch and Peter Mörters
      Adv. in Appl. Probab. 44, No. 2, 583-601 (2012) 
      Preprint
    • Random networks with sublinear preferential attachment: the giant component
      joint work with Peter Mörters
      Ann. Probab. 41, No. 1, 329-384 (2013), DOI 10.1214/11-AOP697
      Preprint
    • Random Networks with Concave Preferential Attachment Rule
      joint work with Peter Mörters
      Jahresber Dtsch Math-Ver 113, No. 1, 21-40 (2011), DOI 10.1365/s13291-010-0011-6
    • Random networks with sublinear preferential attachment: Degree evolutions
      joint work with Peter Mörters
      Electron. J. Probab. 14, 1222-1267 (2009)
      PDF

    Numerical integration / Quadrature of SDEs

    • Multilevel Monte Carlo for Lévy-driven SDEs: central limit theorems for adaptive Euler schemes
      joint work with Sangmeng Li
      Ann. Appl. Probab. 26, No. 1, 136-185 (2016)
      PDF
    • Quadrature for self-affine distributions on R^d
      joint work with Thomas Müller-Gronbach
      Found. Comput. Math. 15, No. 6, 1465-1500 (2015), DOI 10.1007/s10208-014-9233-9
      Preprint
    • On the complexity of computing quadrature formulas for SDEs
      joint work with Thomas Müller-Gronbach and Klaus Ritter
      in Foundations of Computational Mathematics, Budapest 2011 (eds. F. Cucker, T. Krick, A. Pinkus, A. Szanto), LMS Lecture Notes 403, Cambridge University Press, 2012. DOI 10.1017/CBO9781139095402
      Preprint 
    • An Euler-type method for the strong approximation of the Cox-Ingersoll-Ross process
      joint work with Andreas Neuenkirch and Lukas Szpruch
      Proc. R. Soc. A 468, No. 2140, 1105�1115 (2012), DOI 10.1098/rspa.2011.0505
      Preprint
    • Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correction
      Ann. Appl. Probab. 21, No. 1, 283-311 (2011)
      Preprint
    • A multilevel Monte Carlo algorithm for Lévy driven stochastic differential equations
      joint work with Felix Heidenreich
      Stochastic Process. Appl. 121, Mo. 7, 1565-1587 (2011)
      Preprint
    • Infinite-dimensional quadrature and approximation of distributions
      joint work with Jakob Creutzig, Thomas Müller-Gronbach and Klaus Ritter
      Found. Comput. Math. 9, No. 4, 391-429 (2009)
      Preprint

    Small deviations and approximation theory (quantization)

    • Persistence probabilities for an integrated random walk bridge
      joint work with Frank Aurzada and Mikhail Lifshits
      Probab. Math. Statist. 34, No. 1, 1-22 (2014)
      Preprint
    • Constructive quantization: approximation by empirical measures
      joint work with Michael Scheutzow and Reik Schottstedt
      Ann. Inst. Henri Poincaré (B) 49, No. 4, 1183-1203 (2013)
      Preprint
    • Universality of the asymptotics of the one-sided exit problem for integrated processes
      joint work with Frank Aurzada
      Ann. Inst. Henri Poincaré (B) 49, No. 1, 236-251 (2013), DOI 10.1214/11-AIHP427 
      Preprint
    • The high resolution vector quantization problem with Orlicz norm distortion
      joint work with Christian Vormoor
      J. Theor. Probab. 24, No. 2, 517-544 (2011)
      Preprint
    • Small deviations of general Lévy processes
      joint work with Frank Aurzada
      Ann. Probab. 37, No.5, 2066-2092 (2009)
      Preprint
    • High resolution quantization and entropy coding of jump processes
      joint work with Frank Aurzada, Michael Scheutzow and Christian Vormoor
      J. Complexity 25, 163-187 (2009)
      Preprint
    • The coding complexity of Lévy processes
      joint work with Frank Aurzada
      Found. Comput. Math. 9, No. 3, 359-390 (2009)
      Preprint
    • Asymptotic formulae for coding problems and intermediate optimization problems: a review
      in Trends in Stochastic Analysis, edited by Jochen Blath, Peter Morters, and Michael Scheutzow, Cambridge University Press, 187-232, 2009
      Preprint
    • The coding complexity of diffusion processes under supremum norm distortion
      Stochastic Process. Appl. 118, No.6, 917-937 (2008), doi:10.1016/j.spa.2007.07.003
      Preprint
    • The coding complexity of diffusion processes under L^p[0,1]-norm distortion
      Stochastic Process. Appl. 118, No.6, 938-951 (2008), doi:10.1016/j.spa.2007.07.002
      Preprint
    • High-resolution quantization and entropy coding for fractional Brownian motion
      joint work with Michael Scheutzow
      Electron. J. Probab. 11, 700-722 (2006)
      Preprint
    • Probabilities of randomly centered small balls and quantization in Banach spaces
      joint work with Mikhail A. Lifshits
      Ann. Probab. 33, No.4, 1397-1421 (2005)
      PDF
    • Asymptotic behavior of the distortion-rate function for Gaussian processes in Banach spaces
      Bulletin des Sciences Mathématiques 129, No.10, 791-803 (2005)
    • Small ball probabilities around random centers of Gaussian measures and applications to quantization
      J. Theor. Probab. 16, No.2, 427-449 (2003)
    • On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces
      joint work with Franz Fehringer, Anis Matoussi and Michael Scheutzow
      J. Theor. Probab. 16, No.1, 249-265 (2003)

    Stochastic analysis

    • Real self-similar processes started from the origin
      joint work with Leif Döring and Andreas E. Kyprianou
      Ann. Probab. 45, No. 3, 1952-2003 (2017) 
      Preprint
    • A support theorem and a large deviation principle for Kunita flows
      joint work with Georgi Dimitroff
      Stochastics and Dynamics 12, No. 3 (2012)
      Preprint
    • Rough paths analysis of general Banach space-valued Wiener processes
      J. Funct. Anal. 258, No. 9, 2910-2936 (2010)
      Preprint
    • Enlargement of filtrations and continuous Girsanov-type embeddings
      joint work with Stefan Ankirchner and Peter Imkeller
      in Séminaire de Probabilités XL (ed. Catherine Donati-Martin, Michel Émery, Alain Rouault, and Christophe Stricker), LNM1899, Springer, 2007
    • The Shannon information of filtrations and the additional logarithmic utility of insiders
      joint work with Stefan Ankirchner and Peter Imkeller
      Ann. Probab. 34, No.2, 743-778 (2006)
      PDF

    PhD Thesis

    • High resolution coding of stochastic processes and small ball probabilities
      Ph.D. Dissertation (2003)
      PDF