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Currently, I am working on the following projects:

  1. ​Donsker Theorem in Higher Dimension
The goal of this project is to establish convergence ranges between the distributions of the nodal set of the roots of random trigonometric polynomials and a specific Gaussian process, in dimensions greater than or equal to two.
2.  Explosion of stochastic differential equations with switching 
This work studies explosion in stochastic differential equations with switching, where the dynamics depend on both a continuous component and regime changes. We investigate conditions that ensure explosion in finite time and the role of the interaction between noise and the switching structure in this phenomenon.

Preprints 
Stability for the stochastic heat equation with multiplicative noise via finite-dimensional feedback
​arxiv.org/abs/2604.08683

Published papers

  1. Víctor Hernández-Santamaría, Kévin Le Balc’h, Liliana Peralta, Lp-estimates, controllability and local well-posedness for backward SPDEs, to appear in Journal of Differential Equations (2026).
  2. Jorge A. León, Liliana Peralta, Iván Rodríguez, HJB equation for maximization of wealth under insider trading, Mediterr. J. Math. 22, 146 (2025). https://doi.org/10.1007/s00009-025-02921-3
  3. F. Baltazar-Larios, F. Delgado-Vences, L. Peralta, Statistical inference for a stochastic partial differential equation related to an ecological niche, Math. Meth. Appl. Sci.,1–18 (2024).
  4. Víctor Hernández-Santamaría, Kévin Le Balc’h, Liliana Peralta, Global null-controllability for stochastic semilinear parabolic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire (2023).
  5. Laure Coutin, Liliana Peralta, Rates of convergence for the number of zeros of random trigonometric polynomials. Bernoulli 29 (3) 1983 - 2007, (2023).
  6. Víctor Hernández-Santamaría, Liliana Peralta, Controllability results for stochastic coupled systems of fourth- and second-order parabolic equations. J. Evol. Equ. 22, 23 (2022).
  7. Víctor Hernández-Santamaría, Kévin Le Balc’h, Liliana Peralta, Statistical null-controllability of stochastic nonlinear parabolic equations. Stoch PDE: Anal Comp 10, 190–222 (2022).
  8. Liliana Peralta, Distribution Function of the Blow up Time of the Solution of an Anticipating Random Fatigue Equation. Acta. Math. Sin.-English Ser. 37, 551–564 (2021).
  9. Víctor Hernández-Santamaría, Liliana Peralta, Some remarks on the robust Stackelberg controllability for the heat equation with controls on the boundary. Discrete Contin. Dyn. Syst. Ser. B 25, no. 1, 161--190, (2020).
  10. Jorge A. León, Liliana Peralta, Some Feller and Osgood type criteria for semilinear stochastic differential equations. Stoch. Dyn. 17, no. 2, 1750011, 19 pp., (2017).
  11. Jorge A. León, Liliana Peralta, José Villa Morales, On the distribution of explosion time of stochastic differential equations. Boletín de la Sociedad Matemática Mexicana, Vol. 19, no. 2, 125-138, (2013).