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Dr. Konstantinos Dareiotis

  • Position: Lecturer
  • Areas of expertise: Stochastic differential equations; Partial differential equations; Stochastic partial differential and integro-differential equations; Regularization by noise; Numerical methods; Lévy processes
  • Email: K.Dareiotis@leeds.ac.uk
  • Location: 9.14 School of Mathematics

Profile

Employment:

  • University of Leeds, Leeds, UK: Lecturer, Oct 2019—
  • Max Planck Insitute for Mathematics in the Sciences, Leipzig, Germany: Researcher, Sep 2017—Oct 2019
  • Uppsala University, Uppsala, Sweden:  Researcher, Sep 2015—Aug 2017

 

Education:

  •  The University of Edinburgh: PhD in Mathematics under the supervision of Professor István Gyöngy (2015)
  • The University of Edinburgh: Msc in Mathematics under the supervision of Dr Miklós Rásonyi (2011)
  • University of Patras: Bsc in Mathematics (2010)     

 

Publications:

Reports:

  1. O. Butkovksy, K. Dareiotis, M. Gerencsér, K. Lê, Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications, Oberwolfach Reports, DOI: 10.4171/OWR/2022/9

 Journal Publications:

  1. K. Dareiotis, M. Gerencsér, Path-by-path regularisation through multiplicative noise in rough, Young, and ordinary differential equations, Ann. Probab. 52(5): 1864-1902 (2024) https://doi.org/10.1214/24-AOP1686

  2. O. Butkovksy, K. Dareiotis, M. Gerencsér, Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Lévy noise,  to appear in  in Ann. Inst. Henri Poincaré Probab. Stat.  https://arxiv.org/pdf/2204.12926.pdf

  3. O. Butkovksy, K. Dareiotis, M. Gerencsér, Optimal rate of convergence for approximations of SPDEs with non-regular drift,  SIAM J. Numer. Anal. 61 (2023), no. 2, 1103–1137,  https://doi.org/10.1137/21M1454213

  4. K. Dareiotis, M. Gerencsér, K. Lê, Quantifying a convergence theorem of Gyöngy and Krylov,  Ann. Appl. Probab. 33 (2023), no. 3,  60 (65), https://doi.org/10.1214/22-AAP1867

  5. O. Butkovsky, K. Dareiotis, M. Gerencsér, Approximation of SDEs: A stochastic sewing approach,  Probab. Theory Relat. Fields,  (2021),  https://doi.org/10.1007/s00440-021-01080-2

  6. K. Dareiotis, B. Gess, M. Gnann, G. Grün, Non-negative Martingale Solutions to the Stochastic Thin-Film Equation with Nonlinear Gradient Noise,  Arch. Ration. Mech. Anal.,  (2021),    https://doi.org/10.1007/s00205-021-01682-z

  7. K. Dareiotis, M. Gerencsér, B. Gess, Porous media equations with multiplicative space-time white noise, Ann. Inst. H. Poincaré Probab. Statist., 57 (4) 2354 - 2371, (2021). https://doi.org/10.1214/20-AIHP1139

  8. K. Dareiotis, M. Gerencsér,   On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift, Electron. J. Probab., Volume 25 (2020), no. 82, 18 pp. https://projecteuclid.org/euclid.ejp/1594886428 

  9. K. Dareiotis, B. Gess, P. Tsatsoulis, Ergodicity of stochastic porous media equations, SIAM J. Math. Anal., 52 (2020), no.5, 4524–4564. https://epubs.siam.org/doi/pdf/10.1137/19M1278521 

  10. K. Dareiotis, B. Gess, Nonlinear diffusion equations with nonlinear gradient noise,  Electron. J. Probab., Volume 25 (2020), paper no. 35, 43 pp. https://projecteuclid.org/euclid.ejp/1585101794

  11. K. Dareiotis, M. Gerencsér, B. Gess,  Entropy solutions for stochastic porous media equations,  J. Differential Equations  266 (2019), no. 6, 3732-3763. https://www.sciencedirect.com/science/article/pii/S0022039618305333

  12. K. Dareiotis, B. Gess, Supremum estimates for degenerate, quasilinear stochastic partial differential equations. Ann. Inst. Henri Poincaré Probab. Stat. 55 (2019), no. 3, 1765-1796. https://projecteuclid.org/euclid.aihp/1569398885

  13. K. Dareiotis, E. Ekström,  Density symmetries for a class of 2-D diffusions with applications to finance, Stochastic Process. Appl.  129 (2018), no. 2, 452-472.

  14. K. Dareiotis, M. Gerencsér, Local L∞-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs, J. Differential Equations 262 (2017), no. 1, 615-632. http://www.sciencedirect.com/science/article/pii/S0022039616303114

  15. K. Dareiotis, Symmetrization of exterior parabolic problems and probabilistic interpretation, Stoch. Partial Differ. Equ. Anal. Comput. 5 (2017), no. 1, 38-52. http://link.springer.com/article/10.1007/s40072-016-0080-3

  16. K. Dareiotis, On Finite difference schemes for partial integro-differential equations of Lévy type,  J. Comput. Appl. Math. (2019), doi.org/10.1016/j.cam.2019.112587, https://www.sciencedirect.com/science/article/abs/pii/S0377042719305928?via%3Dihub 

  17. K. Dareiotis,  J.M. Leahy,  Finite difference schemes for linear stochastic integro-differential equations. Stochastic Process. Appl. 126 (2016), no. 10, 3202-3234. http://www.sciencedirect.com/science/article/pii/S0304414916300485

  18. K. Dareiotis, C. Kumar, S. Sabanis,  On Tamed Euler Approximations of SDEs Driven by Lévy Noise with Applications to Delay Equations. SIAM J. Numer. Anal. 54 (2016), no. 3, 1840-1872. http://epubs.siam.org/doi/abs/10.1137/151004872

  19. K. Dareiotis, M. Gerencsér,  On the boundedness of solutions of SPDEs. Stoch. PDE: Anal. Comp. 3 (2015), no. 1, 84-102. http://link.springer.com/article/10.1007/s40072-014-0043-5

  20. K. Dareiotis, I. Gyöngy, A comparison principle for stochastic integro-differential equations. Potential Anal. 41 (2014), no. 4, 1203-1222. http://link.springer.com/article/10.1007%2Fs11118-014-9416-7#page-1

Preprints:  

  1. K. Dareiotis, T. Holland , K. Lê,  Regularisation by multiplicative noise for reaction–diffusion equations ,  arXiv:2409.11130 (2024) https://arxiv.org/pdf/2409.11130

  2. K. Dareiotis, M. Gerencsér, K. Lê,  A central limit theorem for the Euler method for SDEs with irregular drifts, arXiv:2309.16339 (2023) https://arxiv.org/pdf/2309.16339.pdf

  3. K. Dareiotis, B. Gess, M. V. Gnann, M. Sauerbrey,  Solutions to the stochastic thin-film equation for initial values with non-full support,  arXiv:2207.03476 (2023) https://arxiv.org/pdf/2305.06017.pdf

  4. K. Dareiotis, A Note On Degenerate Stochastic Integro-Differential Equations,  arXiv: 1406.5649 (2014) http://arxiv.org/pdf/1406.5649.pdf  

Research interests

My research is focused on stochastic analysis and partial differential equations (PDEs). More specifically, I am interested in stochastic PDEs (SPDEs), diffusion/jump-diffusion processes and their connections to PDEs/integro-PDEs, rough differential equations, and applications. I study both qualitative properties of the aforementioned equations such as existence, uniqueness, regularity, and ergodic properties of the solutions but also their numerical approximation. The last few years I mainly work on (i) regularisation by noise phenomena and (ii) degenerate non-linear SPDEs.
 

<h4>Research projects</h4> <p>Any research projects I'm currently working on will be listed below. Our list of all <a href="https://eps.leeds.ac.uk/dir/research-projects">research projects</a> allows you to view and search the full list of projects in the faculty.</p>

Student education

In 2023-2024 I teach  (Advanced) Stochastic Caclulus for Finance  (MATH 3734/MATH5734).

Research groups and institutes

  • Analysis
  • Probability and Financial Mathematics

Current postgraduate researchers

<h4>Postgraduate research opportunities</h4> <p>We welcome enquiries from motivated and qualified applicants from all around the world who are interested in PhD study. Our <a href="https://phd.leeds.ac.uk">research opportunities</a> allow you to search for projects and scholarships.</p>