Publications

• Ren Y., Liu Y., Artola A., Mertz L., Chan R. H., Morel J.M., Efficient Diffusion Training through Parallelization with Truncated Karhunen-Loève Expansion. preprint 

• Ip H.L.F., Mathey C., Mertz L., Wylie J., A control variate method for threshold crossing probabilities of plastic deformation driven by transient coloured noise. preprint 

• Chaintron L.P., Mertz L., Moireau P., Zidani H., Constrained non-linear estimation and links with stochastic filtering. preprint 

• Chen P., González Á.M., Mertz L., An elementary approach based on variational inequalities for modelling a friction-based locomotion problem, Appl. Math. Lett., 160, (2025), 109305. article 

• Mertz L., Nersesyan V., Rissel M., Exponential mixing of constrained random dynamical systems via controllability conditions, SIAM J. Cont. Opt. Vol. 62, (2024), No. 6, p. 3266-3287. article

• Garnier J., Ip H. L. F., Mertz L., Sensitivity analysis of colored noise-driven interacting particle systems, Phys. Rev. E, 110 (2024), 044119. article 

• Garnier J., Mertz L., Computing the diffusivity of a particle subject to dry friction with colored noise, Phys. Rev. E 108 (2023), 045309. article

• Garnier J., Lu Z., Mertz L., A piecewise deterministic Markov process approach modeling a dry friction problem with noise, SIAM J. Appl. Math. Vol. 83 (2023), No. 4, pp. 1392-1421. article

• Chaintron L.P., González Á.M., Mertz L., Moireau P., Mortensen Observer for a class of variational inequalities - Lost equivalence with stochastic filtering approaches, ESAIM Proc. Surveys, September (2023), Vol. 73, p. 130-157. article 

• Garnier, J.; Mertz, L., A control variate method driven by diffusion approximation, Comm. Pure Appl. Math. 75 (2022), no. 3, 455-492. article 

• Bensoussan, A.; Brouste, A.; Cartiaux, F. B.; Mathey, C.; Mertz, L., Mathematical formulation of a dynamical system with dry friction subjected to external forces, Phys. D 421 (2021), Paper No. 132859, 11 pp. article 

• Goerlich R., Manfredi G., Hervieux P.-A., Mertz L., and Genet C., Probing quantum effects with classical stochastic analogs, Phys. Rev. Research 3 (2021), 033203. article 

• Rosales-Cabara Y., Manfredi G., Schnoering G., Hervieux P.-A., Mertz L., and Genet C., Optimal protocols and universal time-energy bound in Brownian thermodynamics, Phys. Rev. Research 2 (2020), 012012(R). article 

• Mertz, L.; Pironneau, O., Numerical analysis of degenerate Kolmogorov equations of constrained stochastic Hamiltonian systems, Comput. Math. Appl. 78 (2019), no. 8, 2719-2733. article 

• Lauriere, M.; Li, Z.; Mertz, L.; Wylie, J.; Zuo, S, Free boundary value problems and HJB equations for the stochastic optimal control of elasto-plastic oscillators, ESAIM Proc. Surveys, 65, EDP Sciences, Les Ulis, 2019, 425-444. article 

• Mertz, L.; Stadler, G.; Wylie, J., A Feynman-Kac formula approach for computing expectations and threshold crossing probabilities of non-smooth stochastic dynamical systems, Phys. D 397 (2019), 25-38. article 

• Laurière, M.; Mertz, L., Penalization of nonsmooth dynamical systems with noise: ergodicity and asymptotic formulae for threshold crossings probabilities, SIAM J. Appl. Dyn. Syst. 18 (2019), no. 2, 853-880. article 

• Huang, J. M.; Zhong, J.-Q.; Zhang, J.; Mertz, L., Stochastic dynamics of fluid-structure interaction in turbulent thermal convection, J. Fluid Mech. 854 (2018), R5, 13 pp. article 

• Feau, C.; Laurière, M.; Mertz, L., Asymptotic formulae for the risk of failure related to an elasto-plastic problem with noise, Asymptot. Anal. 106 (2018), no. 1, 47-60. article 

• Bensoussan, A.; Mertz, L.; Yam, S. C. P., Nonlocal boundary value problems of a stochastic variational inequality modeling an elasto-plastic oscillator excited by a filtered noise, SIAM J. Math. Anal. 48 (2016), no. 4, 2783-2805. article 

• Laurière, M.; Mertz, L., Penalization of a stochastic variational inequality modeling an elasto-plastic problem with noise, ESAIM Proc. Surveys, 48, EDP Sciences, Les Ulis, 2015, 226-247. article 

• Mertz, L.; Bensoussan, A., Degenerate Dirichlet problems related to the ergodic property of an elasto-plastic oscillator excited by a filtered white noise, IMA J. Appl. Math. 80 (2015), no. 5, 1387-1408. article 

• Bensoussan, A.; Feau, C.; Mertz, L.; Yam, S. C. P., An analytical approach for the growth rate of the variance of the deformation related to an elasto-plastic oscillator excited by a white noise, Appl. Math. Res. Express. AMRX(2015), no. 1, 99-128. article 

• Jasso-Fuentes, H.; Mertz, L.; Yam, S. C. P., Approximate solutions of a stochastic variational inequality modeling an elasto-plastic problem with noise, Appl. Math. Res. Express. AMRX(2014), no. 1, 52-73. article 

• Mertz, L.; Feau, C., An empirical study on plastic deformations of an elasto-plastic problem with noise, Probabilistic Engineering Mechanics. 30, (2012) p. 60-69. article 

• Bensoussan, A.; Jasso-Fuentes, H.; Menozzi, S.; Mertz, L., Asymptotic analysis of stochastic variational inequalities modeling an elasto-plastic problem with vanishing jumps, Asymptot. Anal. 80 (2012), no. 1-2, 171-187. article 

• Bensoussan, A.; Mertz, L.; Yam, S. C. P., Long cycle behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise, C. R. Math. Acad. Sci. Paris 350 (2012), no. 17-18, 853-859. article 

• Bensoussan, A.; Mertz, L., An analytic approach to the ergodic theory of a stochastic variational inequality, C. R. Math. Acad. Sci. Paris 350 (2012), no. 7-8, 365-370. article 

• Bensoussan, A.; Mertz, L.; Pironneau, O.; Turi, J.: An ultra weak finite element method as an alternative to a Monte Carlo method for an elasto-plastic problem with noise, SIAM J. Numer. Anal. 47 (2009), no. 5, 3374-3396. article 

Research Grants

Ongoing

• HKSAR-GRF 9043566 (CityU 11302823) (01-2024 to 12-2026). Efficient Monte Carlo methods: control variate for stochastic differential equations, multiscale and constrained dynamics.

• NSFC-SRI 12271364 (01-2023 to 12-2026). 非平滑系统的建模、扩散近似和随机控制 - Modelling, diffusion approximation and stochastic control of non-smooth systems.

Completed

• NSFC 11650110432 (01-2017 to 12-2018). Computational methods for non-smooth dynamical systems excited by random forces.

• NSFC 11601335 (01-2017 to 12-2019). Stochastic control methods for probabilistic engineering mechanics.

Conferences & Seminars

• ERC ELISA Probability Seminar, December 9, 2024, Laboratoire J.A. Dieudonné, Université Côte d'Azur, Nice, France.

• CityU-SJTU Joint Workshop, November 23-24, 2024, City University of Hong Kong, China. (Invited talk).

• 10th International Congress on Industrial and Applied Mathematics, August 20-25, 2023, Waseda University, Tokyo, Japan. (Invited talk).

• 21st INFORMS Applied Probability Society Conference, June 28-30, 2023, Nancy, France. (Contributed talk).

• 14th World Congress in Computational Mechanics (WCCM) and ECCOMAS Congress, January 11 – 15, 2021, Virtual Congress. (Invited talk).

• International Conference on Applied Mathematics, June 4-8, 2018, Hong Kong, China. (Invited talk).  

• International Conference on Moving Interfaces and Related Phenomena in Mathematics and Physics, March 31 - April 2, 2017, Shanghai, China.