Fernanda Andrade da Silva
Email • PhD in Mathematics, USP
Differential equations and stochastic analysis
Visiting Scientist
University of Sao Paulo, Brazil
Host: Enrique Zuazua
Room 03.311 | FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship
Friedrich-Alexander-Universität Erlangen-Nürnberg
Naturwissenschaftliche Fakultät. Department Mathematik
Research Gate | ORCID | Google Scholar
I am a visiting scientist at FAU DCN-AvH, the Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at Friedrich-Alexander-Universität Erlangen-Nürnberg, Bavaria (Germany).
I received my PhD from the University of Sao Paulo (Brazil) in 2021.
My research lies in the field of differential equations and stochastic analysis, with particular emphasis on the theory of generalized ordinary differential equations (GODEs) and their extensions to stochastic frameworks. My work explores the interaction between integral theory, functional differential equations, stability theory, and control theory, focusing on the qualitative behavior of solutions and on systems that involve highly irregular or non-absolutely integrable functions.
A central aspect of my research concerns differential equations formulated through the Kurzweil integral, which provides a powerful framework capable of encompassing a broad class of differential and integral equations. This approach allows the treatment of problems that cannot be handled using classical integrability assumptions and offers a unifying perspective for several types of equations, including measure differential equations, impulsive equations, and dynamic equations on time scales.
More recently, my research has extended to the study of generalized stochastic equations, a new class of equations that broadens the scope of classical stochastic differential equations. In this context, I investigate stability, boundedness, controllability, and qualitative behavior of solutions, often employing techniques based on Lyapunov functionals and functional analytic methods.
Overall, my work aims to contribute to the development of a robust theoretical framework for deterministic and stochastic systems with irregular dynamics, with connections to probability theory, functional analysis, and mathematical physics.
Research interests
A central aspect of my research concerns differential equations formulated through the Kurzweil integral, which provides a powerful framework capable of encompassing a broad class of differential and integral equations. This approach allows the treatment of problems that cannot be handled using classical integrability assumptions and offers a unifying perspective for several types of equations, including measure differential equations, impulsive equations, and dynamic equations on time scales.
More recently, my research has extended to the study of generalized stochastic equations, a new class of equations that broadens the scope of classical stochastic differential equations. In this context, I investigate stability, boundedness, controllability, and qualitative behavior of solutions, often employing techniques based on Lyapunov functionals and functional analytic methods.
Overall, my work aims to contribute to the development of a robust theoretical framework for deterministic and stochastic systems with irregular dynamics, with connections to probability theory, functional analysis, and mathematical physics.
Projects
Publications
2025
- Silva, F. A. D., Gonzalez, K., & Jord\~ao, T. (2025). Asymptotic analysis on a non-standard Hilbert space of non-absolutely integrable functions. (Unpublished, Submitted). arXiv: 2508.19225
2024
- Andrade da Silva, F., Bonotto, E. M., & Federson, M. (2024). Stability for generalized stochastic equations. Stochastic Processes Appl., 173, 14. https://doi.org/10.1016/j.spa.2024.104358
2022
- Andrade da Silva, F., Federson, M., & Toon, E. (2022). Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron \(\Delta\)-integrals. Bull. Math. Sci., 12(3), 47. https://doi.org/10.1142/S1664360721500119
- Andrade da Silva, F., Federson, M., & Toon, E. (2022). Stability, boundedness and controllability of solutions of measure functional differential equations. J. Differ. Equations, 307, 160–210. https://doi.org/10.1016/j.jde.2021.10.044
2021
- Andrade da Silva, F., Federson, M., Grau, R., & Toon, E. (2021). Converse Lyapunov theorems for measure functional differential equations. J. Differ. Equations, 286, 1–46. https://doi.org/10.1016/j.jde.2021.02.060
