Publications

  • Well-posedness of state-dependent rank-based interacting systems. H. Guérin, N. Krell. Preprint (2026) 
    • @misc{GK2026statedependentrankbasedinteracting,
      title={Well-posedness of state-dependent rank-based interacting systems}, 
      author={Hélène Guérin and Nathalie Krell},
      year={2026},
      eprint={2601.06383},
      archivePrefix={arXiv},
      primaryClass={math.PR},
      url={https://arxiv.org/abs/2601.06383}, 
}
    arXiv

  • A stochastic epidemic model with memory of the last infection and waning immunity. H. Guérin, A.B. Zotsa-Ngoufack. Preprint (2025) 
    • @misc{GZN2025stochasticepidemicmodelmemory,
      title={A stochastic epidemic model with memory of the last infection and waning immunity}, 
      author={Hélène Guérin and Arsene Brice Zotsa-Ngoufack},
      year={2025},
      eprint={2505.00601},
      archivePrefix={arXiv},
      primaryClass={math.PR},
      url={https://arxiv.org/abs/2505.00601}, 
}
    arXiv

  • Optimal Withdrawals in a Diffusion Model with State-Dependent Control Rates. H. Guérin, D. Mata, J.F. Renaud, A. Roch. SIAM Journal on Control and Optimization (2026) 10.1137/24M1672614 
    • @article{GMRR-2026.Optimal-Control-diffusion,
author = {Gu\'{e}rin, H\'{e}l\`{e}ne and Mata, Dante and Renaud, Jean-Fran\c{c}ois and Roch, Alexandre},
title = {Optimal Withdrawals in a Diffusion Model with State-Dependent Control Rates},
journal = {SIAM Journal on Control and Optimization},
volume = {64},
number = {2},
pages = {906-930},
year = {2026},
doi = {10.1137/24M1672614},
URL = {https://doi.org/10.1137/24M1672614},
}
    arXiv

  • Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds. H. Guérin, D.T. Nguyen, V.C. Tran. Advances in Applied Probability (2026) 10.1017/apr.2026.10060 
    • @article{guerin-nguyen-tran-2026.laplacian,
      title={Strong uniform convergence of Laplacians of random geometric and directed kNN graphs on compact manifolds}, 
	  DOI={10.1017/apr.2026.10060}, 
	  journal={Advances in Applied Probability}, 
	  author={Guérin, Héléne and Nguyen, Dinh-To{à}n and Tran, Viet Chi}, 
	  year={2026}, 
	  pages={1–36}}
    arXiv

  • Measure estimation on a manifold explored by a diffusion process. V. Divol, H. Guérin, D.T. Nguyen, V.C. Tran. Probability Theory and Related Fields (2025) 10.1007/s00440-025-01437-x 
    • @article{DGNT-estimationmanifold-2025,
      title={Measure estimation on a manifold explored by a diffusion process}, 
      author={Vincent Divol and Hélène Guérin and Dinh-Toan Nguyen and Viet Chi Tran},
      year={2025},
	  journal={Probab. Theory Relat. Fields},
	  fjournal={Probability Theory and Related Fields},
      doi={10.1007/s00440-025-01437-x},
      url={https://doi.org/10.1007/s00440-025-01437-x},}
    arXiv

  • A fixed-point equation approach for the superdiffusive elephant random walk. H. Guérin, L. Laulin, K. Raschel. To appear in Annales de l’Institut Henri Poincaré Probab. Statist. (2025) 
    • @misc{guerin-laulin-raschel-2023.erw,
      title={A fixed-point equation approach for the superdiffusive elephant random walk}, 
      author={Hélène Guérin and Lucile Laulin and Kilian Raschel},
      year={2023},
      eprint={2308.14630},
      archivePrefix={arXiv},
      primaryClass={math.PR}
	}
    arXiv

  • On the limit law of the superdiffusive elephant random walk. H. Guérin, L. Laulin, K. Raschel, T. Simon. Electronic Journal of Probability (2025) 10.1214/25-EJP1362 
    • @article{GLKT-2025-limitlawERW,
author = {H{\'e}l{\`e}ne Gu{\'e}rin and Lucile Laulin and Kilian Raschel and Thomas Simon},
title = {{On the limit law of the superdiffusive elephant random walk}},
volume = {30},
journal = {Electronic Journal of Probability},
number = {none},
publisher = {Institute of Mathematical Statistics and Bernoulli Society},
pages = {1 -- 25},
keywords = {algebraic ordinary differential equation, elephant random walk, incomplete Beta function, Log-concavity, Mittag-Leffler function, strong Tauberian theorem, superdiffusive limit, Unimodality},
year = {2025},
doi = {10.1214/25-EJP1362},
URL = {https://doi.org/10.1214/25-EJP1362}
}
    arXiv

  • Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model. F. Foutel-Rodier, A. Charpentier, H. Guérin. Journal of Mathematical Biology (2025) 10.1007/s00285-024-02171-z 
    • 	  @article{foutelrodier-charpentier-guerin-2025.vaccin,
      TITLE={Optimal Vaccination Policy to Prevent Endemicity: A Stochastic Model}, 
      AUTHOR={Félix Foutel-Rodier and Arthur Charpentier and Hélène Guérin},
      JOURNAL={ J. Math. Biol.},
      FJOURNAL={Journal of Mathematical Biology},
      VOLUME = {90},
      NUMBER={10},
      YEAR = {2025},
      DOI = {10.1007/s00285-024-02171-z},
      URL = {https://doi.org/10.1007/s00285-024-02171-z},
      }
    arXiv

  • Elephant polynomials. H. Guérin, L. Laulin, K. Raschel. Aequationes mathematicae (2024) 10.1007/s00010-024-01095-9 
    • @article{guerin-laulin-raschel-2024.Elephant-poly,
      TITLE={Elephant polynomials}, 
      AUTHOR={Hélène Guérin and Lucile Laulin and Kilian Raschel},
      YEAR={2024},
      JOURNAL={Aequationes mathematicae},
      FJOURNAL={Aequationes mathematicae},
      DOI={10.1007/s00010-024-01095-9},
      URL={https://doi.org/10.1007/s00010-024-01095-9},
	}
    arXiv

  • On the distribution of cumulative Parisian ruin. H. Guérin, J.F. Renaud. Insurance: Mathematics & Economics (2017) 10.1016/j.insmatheco.2017.01.009 
    • @article {guerin-renaud-2017.parisian,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene and Renaud, Jean-Fran\c{c}ois},
     TITLE = {On the distribution of cumulative {P}arisian ruin},
   JOURNAL = {Insurance Math. Econom.},
  FJOURNAL = {Insurance: Mathematics \& Economics},
    VOLUME = {73},
      YEAR = {2017},
     PAGES = {116--123},
   MRCLASS = {91B30 (60J75)},
       DOI = {10.1016/j.insmatheco.2017.01.009},
       URL = {https://doi.org/10.1016/j.insmatheco.2017.01.009},
}
    arXiv

  • Long time behavior of telegraph processes under convex potentials. J. Fontbona, H. Guérin, F. Malrieu. Stochastic Processes and their Applications (2016) 10.1016/j.spa.2016.04.002 
    • @article {fontbona-guerin-malrieu-2016.telegraphconvex,
    AUTHOR = {Fontbona, Joaquin and Gu\'{e}rin, H\'{e}l\`ene and Malrieu,
              Florent},
     TITLE = {Long time behavior of telegraph processes under convex
              potentials},
   JOURNAL = {Stochastic Process. Appl.},
  FJOURNAL = {Stochastic Processes and their Applications},
    VOLUME = {126},
      YEAR = {2016},
    NUMBER = {10},
     PAGES = {3077--3101},
   MRCLASS = {60F17 (60G50 60J05 60J25 60J60)},
       DOI = {10.1016/j.spa.2016.04.002},
       URL = {https://doi.org/10.1016/j.spa.2016.04.002},}
    arXiv

  • Joint distribution of a spectrally negative Lévy process and its occupation time, with step option pricing in view. H. Guérin, J.F. Renaud. Advances in Applied Probability (2016) 10.1017/apr.2015.17 
    • @article {guerin-renaud-2016.occupation,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene and Renaud, Jean-Fran\c{c}ois},
     TITLE = {Joint distribution of a spectrally negative {L}\'{e}vy process
              and its occupation time, with step option pricing in view},
   JOURNAL = {Adv. in Appl. Probab.},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {48},
      YEAR = {2016},
    NUMBER = {1},
     PAGES = {274--297},
   MRCLASS = {60G51 (91G20)},
       URL = {http://projecteuclid.org/euclid.aap/1457466166},
}
    arXiv

  • On the depletion problem for an insurance risk process: new non-ruin quantities in collective risk theory. Z. Ben-Salah, H. Guérin, M. Morales, H.O. Firouzi. European Actuarial Journal (2015) 10.1007/s13385-015-0112-9 
    • @article {bensalah-al-2015.depletion,
    AUTHOR = {Ben-Salah, Zied and Gu\'{e}rin, H\'{e}l\`ene and Morales,
              Manuel and Firouzi, Hassan Omidi},
     TITLE = {On the depletion problem for an insurance risk process: new
              non-ruin quantities in collective risk theory},
   JOURNAL = {Eur. Actuar. J.},
  FJOURNAL = {European Actuarial Journal},
    VOLUME = {5},
      YEAR = {2015},
    NUMBER = {2},
     PAGES = {381--425},
   MRCLASS = {99-01},
       DOI = {10.1007/s13385-015-0112-9},
       URL = {https://doi.org/10.1007/s13385-015-0112-9},
}
    arXiv

  • Quantitative estimates for the long-time behavior of an ergodic variant of the telegraph process. J. Fontbona, H. Guérin, F. Malrieu. Advances in Applied Probability (2012) 10.1239/aap/1354716586 
    • @article {fontbona-guerin-malrieu-2012.telegraph,
    AUTHOR = {Fontbona, Joaquin and Gu\'{e}rin, H\'{e}l\`ene and Malrieu,
              Florent},
     TITLE = {Quantitative estimates for the long-time behavior of an
              ergodic variant of the telegraph process},
   JOURNAL = {Adv. in Appl. Probab.},
  FJOURNAL = {Advances in Applied Probability},
    VOLUME = {44},
      YEAR = {2012},
    NUMBER = {4},
     PAGES = {977--994},
   MRCLASS = {60J25 (60F17 60J75 93E15)},
       URL = {http://projecteuclid.org/euclid.aap/1354716586},
}
    arXiv

  • Long time behavior of diffusions with Markov switching. J.B. Bardet, H. Guérin, F. Malrieu. ALEA. Latin American Journal of Probability and Mathematical Statistics (2010) .pdf 
    • @article {bardet-guerin-malrieu-2010.switching,
    AUTHOR = {Bardet, Jean-Baptiste and Gu\'{e}rin, H\'{e}l\`ene and
              Malrieu, Florent},
     TITLE = {Long time behavior of diffusions with {M}arkov switching},
   JOURNAL = {ALEA Lat. Am. J. Probab. Math. Stat.},
  FJOURNAL = {ALEA. Latin American Journal of Probability and Mathematical
              Statistics},
    VOLUME = {7},
      YEAR = {2010},
     PAGES = {151--170},
   MRCLASS = {60J60 (60H25 60J75)},
}
    arXiv

  • On the Laplace transform of perpetuities with thin tails. J.B. Bardet, H. Guérin, F. Malrieu. ArXiv (2009) 
    • @misc{bardet-guerin-malrieu-2009.perpetuities,
      TITLE={On the Laplace transform of perpetuities with thin tails}, 
      AUTJOR={Jean-Baptiste Bardet and Hélène Guerin and Florent Malrieu},
      YEAR={2009},
      EPRINT={0912.3232},
      archivePrefix={arXiv},
      primaryClass={math.PR}
}
    arXiv

  • Measurability of optimal transportation and strong coupling of martingale measures. J. Fontbona, H. Guérin, S. Méléard. Electronic Communications in Probability (2010) 10.1214/ECP.v15-1534 
    • @article {fontbona-guerin-meleard-2010.optimaltransp,
    AUTHOR = {Fontbona, Joaquin and Gu\'{e}rin, H\'{e}l\`ene and
              M\'{e}l\'{e}ard, Sylvie},
     TITLE = {Measurability of optimal transportation and strong coupling of
              martingale measures},
   JOURNAL = {Electron. Commun. Probab.},
  FJOURNAL = {Electronic Communications in Probability},
    VOLUME = {15},
      YEAR = {2010},
     PAGES = {124--133},
   MRCLASS = {49Q20 (60G57)},
       DOI = {10.1214/ECP.v15-1534},
       URL = {https://doi.org/10.1214/ECP.v15-1534},
}
    arXiv

  • Measurability of optimal transportation and convergence rate for Landau type interacting particle systems. J. Fontbona, H. Guérin, S. Méléard. Probability Theory and Related Fields (2009) 10.1007/s00440-007-0128-4 
    • @article {fontbona-guerin-meleard-2009.landau,
    AUTHOR = {Fontbona, Joaquin and Gu\'{e}rin, H\'{e}l\`ene and
              M\'{e}l\'{e}ard, Sylvie},
     TITLE = {Measurability of optimal transportation and convergence rate
              for {L}andau type interacting particle systems},
   JOURNAL = {Probab. Theory Related Fields},
  FJOURNAL = {Probability Theory and Related Fields},
    VOLUME = {143},
      YEAR = {2009},
    NUMBER = {3-4},
     PAGES = {329--351},
   MRCLASS = {60K35 (49Q20 60G07 60J65)},
       DOI = {10.1007/s00440-007-0128-4},
       URL = {https://doi.org/10.1007/s00440-007-0128-4},
}
    arXiv

  • On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity. N. Fournier, H. Guérin. Journal of Statistical Physics (2008) 10.1007/s10955-008-9511-5 
    • @article {fournier-guerin-2008.boltz,
    AUTHOR = {Fournier, Nicolas and Gu\'{e}rin, H\'{e}l\`ene},
     TITLE = {On the uniqueness for the spatially homogeneous {B}oltzmann
              equation with a strong angular singularity},
   JOURNAL = {J. Stat. Phys.},
  FJOURNAL = {Journal of Statistical Physics},
    VOLUME = {131},
      YEAR = {2008},
    NUMBER = {4},
     PAGES = {749--781},
   MRCLASS = {35F20 (35B30 82C40)},
       DOI = {10.1007/s10955-008-9511-5},
       URL = {https://doi.org/10.1007/s10955-008-9511-5},
}
    arXiv

  • Estimates for the density of a nonlinear Landau process. H. Guérin, S. Méléard, E. Nualart. Journal of Functional Analysis (2006) 10.1016/j.jfa.2006.01.017 
    • @article {guerin-meleard-nualart-2006.densitylandau,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene and M\'{e}l\'{e}ard, Sylvie and
              Nualart, Eulalia},
     TITLE = {Estimates for the density of a nonlinear {L}andau process},
   JOURNAL = {J. Funct. Anal.},
  FJOURNAL = {Journal of Functional Analysis},
    VOLUME = {238},
      YEAR = {2006},
    NUMBER = {2},
     PAGES = {649--677},
   MRCLASS = {60H07 (60H10 60H20)},
       DOI = {10.1016/j.jfa.2006.01.017},
       URL = {https://doi.org/10.1016/j.jfa.2006.01.017},
}
    arXiv

  • Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilistic interpretation. H. Guérin. ESAIM. Probability and Statistics (2004) 10.1051/ps:2003018 
    • @article {guerin-2004.pointconvboltz,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene},
     TITLE = {Pointwise convergence of {B}oltzmann solutions for grazing
              collisions in a {M}axwell gas via a probabilistic
              interpretation},
   JOURNAL = {ESAIM Probab. Stat.},
  FJOURNAL = {ESAIM. Probability and Statistics},
    VOLUME = {8},
      YEAR = {2004},
     PAGES = {36--55},
   MRCLASS = {82C40 (60H07 60H10 60J75)},
       DOI = {10.1051/ps:2003018},
       URL = {https://doi.org/10.1051/ps:2003018},
}

  • Convergence from Boltzmann to Landau processes with soft potential and particle approximations. H. Guérin, S. Méléard. Journal of Statistical Physics (2003) 10.1023/A:1022858517569 
    • @article {guerin-meleard-2003.convboltz,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene and M\'{e}l\'{e}ard, Sylvie},
     TITLE = {Convergence from {B}oltzmann to {L}andau processes with soft
              potential and particle approximations},
   JOURNAL = {J. Statist. Phys.},
  FJOURNAL = {Journal of Statistical Physics},
    VOLUME = {111},
      YEAR = {2003},
    NUMBER = {3-4},
     PAGES = {931--966},
   MRCLASS = {82C31 (82C03)},
       DOI = {10.1023/A:1022858517569},
       URL = {https://doi.org/10.1023/A:1022858517569},
					}

  • Solving Landau equation for some soft potentials through a probabilistic approach. H. Guérin. The Annals of Applied Probability (2003) 10.1214/aoap/1050689592 
    • @article {guerin-2003.landau,
    AUTHOR = {Gu\'{e}rin, H\'{e}l\`ene},
     TITLE = {Solving {L}andau equation for some soft potentials through a
              probabilistic approach},
   JOURNAL = {Ann. Appl. Probab.},
  FJOURNAL = {The Annals of Applied Probability},
    VOLUME = {13},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {515--539},
   MRCLASS = {82C40 (60H10 60H30 82C31)},
       DOI = {10.1214/aoap/1050689592},
       URL = {https://doi.org/10.1214/aoap/1050689592},
}

  • Existence and regularity of a weak function-solution for some Landau equations with a stochastic approach. H. Guérin. Stochastic Processes and their Applications (2002) 10.1016/S0304-4149(02)00107-2 
    • @article {guerin-2002.weaklandau,
    AUTHOR = {Gu\'{e}rin, H.},
     TITLE = {Existence and regularity of a weak function-solution for some
              {L}andau equations with a stochastic approach},
   JOURNAL = {Stochastic Process. Appl.},
  FJOURNAL = {Stochastic Processes and their Applications},
    VOLUME = {101},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {303--325},
   MRCLASS = {60H30 (35R60 60H07 82C40)},
       DOI = {10.1016/S0304-4149(02)00107-2},
       URL = {https://doi.org/10.1016/S0304-4149(02)00107-2},
}

Thesis

  • Probabilistic approach of the Landau equation. PhD thesis. Université Paris X - Nanterre, Modal'X (2002). Supervisor: Sylvie Méléard. HAL_logo

  • Probabilistic models in physics, biology and actuarial science. Habilitation à diriger des recherches. Université de Rennes 1, Institut de Mathématiques de Rennes (2019) HAL_logo


Hélène Guérin

  Département de Mathématiques
  Université du Québec à Montréal

guerin.helene@uqam.ca
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