Stefan Geiss - Research



PREPRINTS (ArXiv)

  1. Convergence rate for random walk approximations of mean field BSDEs.
    With B. Djehiche, H. Geiss, C. Labart, and J. Nykänen.
    arXiv:2409.14212, 2024 .
  2. On the sharpness of embeddings of Hölder spaces into Gaussian Besov spaces.
    arXiv:2009.14112, 2020.
  3. On Riemann-Liouville operators, BMO, gradient estimates in the Lévy-Itô space, and approximation.
    With T. Nguyen.
    arXiv:2009.00899, 2020.

IN REVISION

  1. On Riemann-Liouville type operators, bounded mean oscillation, gradient estimates and approximation
    on the Wiener space.
    With T. Nguyen, 2024.

MONOGRAPHS

  1. Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs.
    With J. Ylinen.
    arXiv1409.532, Memoirs AMS 1335 (2021).

ARTICLES

  1. On decoupling in Banach spaces.
    With S. Cox.
    Journal of Theoretical Probability, doi.org/10.1007/s10959-021-01085-6.
  2. Donsker-Type Theorem for BSDEs: Rate of Convergence.
    With P. Briand, C. Geiss and C. Labart.
    Bernoulli, ArXiv:1908.01188.
  3. Weighted Bounded Mean Oscillation applied to Backward Stochastic Differential Equations.
    With J. Ylinen.
    arXiv:1501.01183, Stochastic Process. Appl. 130(2020)37111–3752.
  4. Permutation invariant functionals of Lévy processes.
    With F. Baumgartner.
    Trans. Amer. Math. Soc. 369, 8607-8641, 2017.
  5. First time to exit of a continuous Itô process: general moment estimates and L1-convergence rate for discrete time approximations.
    With B. Bouchard and E. Gobet.
    Bernoulli 23 (2017), no. 3, 1631–1662.
  6. Fractional smoothness of functionals of diffusion processes under a change of measure.
    With E. Gobet.
    Electronic Communications in Probability Vol. 19, (35), 2014.
  7. On fractional smoothness and Lp-approximation on the Gaussian space.
    With A. Toivola.
    Annals of Probability Vol. 43, pp. 605-638, 2015.
  8. A note on Malliavin fractional smoothness for Lévy processes and approximation.
    With C. Geiss and E. Laukkarinen.
    Potential Analysis 39, pp.203-230, 2013.
  9. Generalized fractional smoothness and Lp-variation of BSDEs with non-Lipschitz terminal conditions.
    With C. Geiss and E. Gobet.
    Stochastic Processes and their Applications 122, pp.2078-2116, 2012.
  10. Extrapolation of vector valued rearrangement operators.
    With P. F. X. Müller.
    J. Lond. Math. Soc.80(3), pp.798-814, 2009.
  11. Weak convergence of error processes in discretizations of stochastic integrals and Besov spaces.
    With A. Toivola.
    Bernoulli 15 (4), pp.925-954, 2009.
  12. On singular integrals and martingale transforms.
    With S. Montgomery-Smith and E.Saksman.
    Transactions AMS, Vol.362 (2), pp.553-575, 2010.
  13. Haar type and Carleson constants.
    With P. F. X. Müller.
    Bulletin of the London Mathematical Society 40, pp.432-438, 2008.
  14. Interpolation and approximation in L2(γ).
    With M. Hujo.
    Journal of Approximation Theory 144, pp.213-232, 2007.
  15. A remark on extrapolation of rearrangement operators on dyadic Hs, 0 < s ≤ 1.
    With With P. F. X. Müller and V. Pillwein.
    Studia Math. 171, pp.196-205, 2005.
  16. On an approximation problem for stochastic integrals where random time nets do not help.
    With C. Geiss.
    Stoch. Proc. Appl. 116, pp.407-422, 2006.
  17. On approximation of a class of stochastic integrals and interpolation.
    With C. Geiss.
    Stochastics and Stochastics Reports 76, pp.339-362, 2004.
  18. Weighted BMO and discrete time hedging within the Black-Scholes model.
    Prob. Theory Related Fields 132, pp.39-73, 2005.
  19. Quantitative approximation of certain stochastic integrals.
    Stochastics and Stochastics Reports 73, pp.241-270, 2002.
  20. On the approximation of stochastic integrals and weighted BMO.
    Stochastic Processes and Related Topics, Eds. R. Buckdahn, H. J. Engelbert, M. Yor. Stochastics Monographs. Taylor-Francis Books, 2002.
  21. A general contraction principle for vector valued martingales.
    Prob. and Math. Statistics, Vol.20, pp.93-120, 2000.
  22. Contraction principles for vector valued martingales with respect to random variables having exponential tail with exponent 2<α<∞.
    J. Theor. Prob. 14, pp.39-59, 2001.
  23. Absolutely Lexpq-summing norms of diagonal operators in lr and limit orders of Lexp-summing operators.
    Math. Nachr. Vol. 223, pp- 33-48, 2001.
  24. On BMO-spaces of adapted sequences .
    Séminaire d'initiation à l'analyse, année 1997/99, Publications mathématiques de l'Université Paris VI, 10 pp.
  25. Espaces BMOΦ0,s et Extrapolation.
    Séminaire d'initiation à l'analyse, année 1996/97, Publications mathématiques de l'Université Paris VI, 7 pp.
  26. A counterexample concerning the relation between decoupling constants and UMD-constants.
    Trans. Amer. Math. Soc. 351, pp.1355-1375, 1999.
  27. Operators on martingales, Φ-summing operators, and the contraction principle
    Prob. and Math. Statistics 18.1, pp.149-171, 1998.
  28. BMOψ-spaces and applications to extrapolation theory.
    Studia Math. 122(3), pp.235-274, 1997.
  29. Absolutely LΦ-summing operators and an application to the contraction principle.
    Séminaire d'initiation à l'analyse, année 1995/96, Publications mathématiques de l'Université Paris VI 11 pp.
  30. Type and Cotype with respect to arbitrary orthonormal systems.
    With M. Junge
    Journal of Approximation Theory 82, pp.399-433, 1995.
  31. Antisymmetric tensor products of nuclear operators on Banach spaces.
    Lecture Notes in Pure and Applied Mathematics 150, M. Dekker, New York 1993.
  32. Antisymmetric tensor products of absolutely p-summing operators
    Journal of Approximation Theory 68, pp.223-246, 1992.
  33. Some relations between s-numbers of operators on Banach spaces.
    Monatshefte für Mathematik 110, pp.217-230, 1990.
  34. Grothendieck numbers and volume ratios of operators on Banach spaces.
    Forum Mathematicum 2, pp.323-340, 1990.
  35. Grothendieck numbers of linear and continuous operators on Banach spaces.
    Mathematische Nachrichten 148, pp.65-79, 1990.
  36. Ein Faktorisierungssatz für mulitlineare Funktionale.
    Mathematische Nachrichten 134, pp. 149-159, 1987.

CHAPTERS/BOOKS

  1. Fractional smoothness and applications in Finance.
    With E. Gobet.
    In 'Advanced Mathematical Methods for Finance', G. Di Nunno and B. Oksendal, editors,
    Springer Verlag. 2011.

PREPRINTS

  1. On decoupling in Banach spaces.
    With S. Cox.
    arXiv:1805.12377, 2018.

OTHER PUBLICATIONS




Department of Mathematics and Statistics, P.O.Box 35 (MaD) FI-40014 University of Jyväskylä, Finland, Phone: +358 408053422