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Torstein Kastberg Nilssen

Førsteamanuensis

 
Kontor:
J2044 ( Universitetsveien 25, Kristiansand )

Arbeidserfaring

  • Oktober 2019. Førsteamanuensis, Universitetet i Agder.
  • Februar 2017 - Oktober 2019. Post-doc ved Technische Universität Berlin, Insitut für Mathematik.
  • November 2015 - Juli 2016. Gjesteforsker ved University of Southern California, Los Angeles.
  • Mars 2014 - Juni 2014. Gjesteforsker ved University of Manchester, Department of Mathematics.
  • Februar 2014 - Januar 2017. Post-doc ved Universitetet i Oslo, Matematisk institutt.
  • Januar 2013 - Juli 2013. Gjesteforsker ved Humbold Universität zu Berlin, Institut für Mathematik.
  • Januar 2010 - Desember 2013. Doktorgradsavhandling ved Universitetet i Oslo, Matematisk institutt.

Faglige interesser

Nonlinear stochastic partial differential equations and variational methods. Pathwise solutions and rough paths. Stochastic (Partial) Differential Equations with irregular coeffcients. The (Stochastic) Transport Equation. Regularizing effect of noise. Malliavin calculus. 

Utvalgte publikasjoner

  • Antoine Hocquet, Torstein Nilssen: An Itô Formula for rough partial differential equations and some applications.
    Potential Analysis (2020) https://doi.org/10.1007/s11118-020-09830-y
  • David Banos, Torstein Nilssen, Frank Proske: Strong existence and higher order Frechet differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift.
    Journal of Dynamics and Differential Equations (2019). https://doi.org/10.1007/s10884-019-09789-4
    Preprint: http://arxiv.org/abs/1511.02717
  • Torstein Nilssen: Rough linear PDE's with discontinuous coeffcients - existence of solutions via regularization by fractional Brownian motion.
    Electron. J. Probab. Volume 25 (2020), paper no. 34, 33 pp.
    Preprint: http://arxiv.org/abs/1509.01154
  • Peter Friz, Torstein Nilssen Wilhelm Stannat: Existence, uniqueness and stability of semilinear rough partial differential equations.
    Journal of Differential Equations, 2019, ISSN 0022-0396, https://doi.org/10.1016/j.jde.2019.09.033.
  • Antoine Hocquet, Torstein Nilssen, Wilhelm Stannat: Generalized Burgers equation with rough transport noise.
    Stochastic Processes and their Applications, 2019, ISSN 0304-4149, https://doi.org/10.1016/j.spa.2019.06.014.
  • Martina Hofmanova, James-Michael Leahy, Torstein Nilssen: On the Navier-Stokes equation perturbed by rough transport noise.
    Journal of Evolution Equations (2018). https://doi.org/10.1007/s00028-018-0473-z
  • Torstein Nilssen: Quasi-linear Stochastic Partial Differential Equations with irregular Coeffcients - Malliavin Regularity of the Solution.
    Stochastic Partial Differential Equations: Analysis and Computations. September 2015, Volume 3, Issue 3, pp 339-359.
  • Salah-Eldin A. Mohammed, Torstein Nilssen, Frank Proske: Sobolev Differentiable Stochastic Flows of SDE`s with Measurable Drift and Applications.
    Ann. Probab. Volume 43, Number 3 (2015), 1535-1576.
  • David Banos, Torstein Nilssen: Malliavin regularity and regularity of densities of SDE's. A classical solution to the stochastic transport equation. Stochastics, (2015), DOI: 10.1080/17442508.2015.1102265.
  • Torstein Nilssen: Regularity of Strong Solutions of one-dimensional SDE's with discontinuous and unbounded drift.
    Stochastics, An International Journal of Probability and Stochastic Processes, Volume 88, 2016 -
    Issue 5
  • Thilo Meyer-Brandis, Torstein Nilssen, Olivier Menoukeu-Pamen, Frank Norbert Proske, Tusheng Zhang: A variational approach to the construction and Malliavin differentiability of strong solutions of SDE's.
    Mathematische Annalen, Springer-Verlag Berlin Heidelberg 201310.1007/s00208-013-0916-3, 2013.

Vitenskapelige publikasjoner

  • Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein (2021). On a rough perturbation of the Navier–Stokes system and its vorticity formulation. The Annals of Applied Probability. ISSN: 1050-5164. 31 (2). s 736 - 777. doi:10.1214/20-AAP1603.
  • Hocquet, Antoine; Nilssen, Torstein (2020). An Itô Formula for rough partial differential equations and some applications. Potential Analysis. ISSN: 0926-2601. 54s 331 - 386. doi:10.1007/s11118-020-09830-y.
  • Nilssen, Torstein (2020). Rough linear PDEs with discontinuous coefficients – existence of solutions via regularization by fractional Brownian motion. Electronic Journal of Probability (EJP). ISSN: 1083-6489. 25s 1 - 33. doi:10.1214/20-EJP437.
  • Hofmanova, Martina; Leahy, James-Michael; Nilssen, Torstein Kastberg (2018). On the Navier–Stokes equation perturbed by rough transport noise. Journal of evolution equations (Printed ed.). ISSN: 1424-3199. 19 (1). s 203 - 247. doi:10.1007/s00028-018-0473-z.
  • Baños, David Ruiz; Nilssen, Torstein Kastberg; Proske, Frank Norbert (2020). Strong Existence and Higher Order Fréchet Differentiability of Stochastic Flows of Fractional Brownian Motion Driven SDEs with Singular Drift. Journal of Dynamics and Differential Equations. ISSN: 1040-7294. 32s 1819 - 1866. doi:10.1007/s10884-019-09789-4.
  • Harang, Fabian Andsem; Proske, Frank Norbert; Nilssen, Torstein Kastberg (2017). Girsanov Theorem for Multifractional Brownian Processes. arXiv.org. ISSN: 2331-8422.
  • Nilssen, Torstein Kastberg; Leahy, James; Hofmanova, Martina (2017). Navier Stokes Equation with Rough Transport Noise. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN: 0806-2439.
  • Baños, David Ruiz; Nilssen, Torstein Kastberg (2016). Malliavin and flow regularity of SDEs. Application to the study of densities and the stochastic transport equation. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN: 1744-2508. 88 (4). s 540 - 566. doi:10.1080/17442508.2015.1102265.
  • Nilssen, Torstein Kastberg (2016). Regularity of strong solutions of one-dimensional SDE’s with discontinuous and unbounded drift. Stochastics: An International Journal of Probability and Stochastic Processes. ISSN: 1744-2508. 88 (5). s 779 - 802. doi:10.1080/17442508.2016.1144755.
  • Nilssen, Torstein Kastberg (2015). Quasi-linear stochastic partial differential equations with irregular coefficients - Malliavin regularity of the solutions.. Stochastics and Partial Differential Equations: Analysis and Computations. ISSN: 2194-0401. doi:10.1007/s40072-015-0053-y.
  • Nilssen, Torstein Kastberg (2015). Rough path continuity equations with discontinuous coefficients - regularization by fractional Brownian motion. arXiv.org. ISSN: 2331-8422. doi:10.1214/20-ejp437.
  • Nilssen, Torstein Kastberg (2015). Rough path transport equation with discontinuous coefficient - regularization by fractional Brownian motion. arXiv.org. ISSN: 2331-8422.
  • Mohammed, Salah-Eldin; Nilssen, Torstein Kastberg; Proske, Frank Norbert (2014). Sobolev differentiable stochastic flows for sdes with singular coefficients: Applications to the transport equation. Annals of Probability. ISSN: 0091-1798. 43 (3). s 1535 - 1576. doi:10.1214/14-AOP909.
  • Banos, David Ruiz; Nilssen, Torstein Kastberg; Proske, Frank Norbert (2015). Strong existence and higher order Fréchet differentiability of stochastic flows of fractional Brownian motion driven SDE's with singular drift. arXiv.org. ISSN: 2331-8422. doi:10.1007/s10884-019-09789-4.
  • Nilssen, Torstein Kastberg; Zhang, Tusheng (2014). A Note on the Malliavin Differentiability of One-Dimensional Reflected Stochastic Differential Equations with Discontinuous Drift. arXiv.org. ISSN: 2331-8422.
  • Menoukeu, Olivier Pamen; Meyer-Brandis, Thilo; Nilssen, Torstein Kastberg; Proske, Frank Norbert; Zhang, Tusheng (2013). A variational approach to the construction and Malliavin differentiability of strong solutions of SDE's. Mathematische Annalen. ISSN: 0025-5831. 357 (2). s 761 - 799. doi:10.1007/s00208-013-0916-3.
  • Flandoli, Franco; Nilssen, Torstein Kastberg; Proske, Frank Norbert (2013). Malliavin differentiability and strong solutions for a class of SDE in Hilbert spaces. Preprint series (Universitetet i Oslo. Matematisk institutt). ISSN: 0806-2439.
  • Nilssen, Torstein (2020). Introduction to rough paths.
  • Nilssen, Torstein (2020). Rough path variational principles for fluid equations.
  • Nilssen, Torstein (2020). Rough path variational principles for fluid equations.
  • Nilssen, Torstein (2020). Rough path variational principles for fluid equations.
  • Nilssen, Torstein (2020). Rough path variational principles for fluid equations.

Ekspertområder

Sist endret: 4.05.2020 10:05