Dr. Konstantinos Dareiotis

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:

 Journal Publications:

  1. O. Butkovsky, K. Dareiotis, M. Gerencsér, Approximation of SDEs: A stochastic sewing approach, Accepted in Probab. Theory Relat. Fields,  (2021),  https://arxiv.org/pdf/1909.07961.pdf

  2. 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

  3. K. Dareiotis, M. Gerencsér, B. Gess, Porous media equations with multiplicative space-time white noise, Accepted in Ann. Inst. Henri Poincaré Probab. Stat.,  (2020),  https://arxiv.org/pdf/2002.12924.pdf 

  4. 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 

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

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

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

  8. 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

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

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

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

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

  13. 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

  14. 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

  15. 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

  16. 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, M. Gerencsér, K. Lê, Quantifying a convergence theorem of Gyöngy and Krylov arXiv:2101.12185 (2021) https://arxiv.org/pdf/2101.12185.pdf

  2. K. Dareiotis, A Note On Degenerate Stochastic Integro-Differential EquationsarXiv: 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, diffusion processes and their connections to PDEs, and their applications. I study both qualitative properties of the aforementioned equations  – such as existence, uniqueness, regularity, and ergodic properties of the solutions — and their numerical approximation.  In the past, my work was focused on stochastic PDEs and stochastic partial integro-differential equations (PIDEs)  related to the non-linear filtering of Itô-Lévy processes (jump-diffusions), numerical analysis for stochastic equations in finite and infinite dimensions, applications of stochastic analysis in finance, and isoperimetric inequalities. Currently I am focused on (i) degenerate non-linear stochastic PDEs related to scaling limits of interacting particle systems with a branching mechanism and (ii) on the regularization by noise with emphasis in numerical analysis. 
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<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 session 2020-2021 I teach Financial Mathematics: Risk (MATH 2535)  and Stochastic Caclulus (MATH 3734).

Research groups and institutes

  • Analysis
  • Probability and Financial Mathematics
<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>
Projects
    <li><a href="//phd.leeds.ac.uk/project/925-regularization-by-noise:-analysis-of-numerics">Regularization-by-noise: Analysis of Numerics</a></li>