Kelvin J. R. Almeida-Sousa
Kelvin J. R. Almeida-Sousa is a Brazilian mathematician with contributions to deterministic and stochastic partial differential equations, numerical analysis, mathematical statistics, and spectral theory.
Biography
Kelvin J. R. Almeida-Sousa is a Brazilian mathematician and postdoctoral fellow in the Stochastic Processes and Mathematical Statistics group at King Abdullah University of Science and Technology (KAUST). Since December 2022, he has been working under the supervision of Professor David Bolin, with research focused on non-Gaussian stochastic partial differential equations and random fields on complex domains, combining tools from numerical analysis, spectral theory, and mathematical statistics.
Kelvin obtained his PhD in Mathematics from the Federal University of Paraíba, Brazil, under the supervision of Professor Alexandre de Bustamante Simas. His doctoral research addressed fractional and measure-theoretic elliptic operators and their applications to deterministic and stochastic partial differential equations, leading to results in regularity theory and spectral analysis. He earned his MSc in Mathematics from the Federal University of Piauí, where his work focused on nonlinear thermoelastic systems with boundary damping.
His current research interests include non-Gaussian SPDE models, finite volume and lumped mass discretization methods, spatial statistics on complex domains such as metric graphs and surfaces, and the theoretical foundations connecting stochastic processes with generalized Sobolev-type spaces.
Research Interests
Kelvin’s research interests are structured along two complementary directions, a theoretical and an applied one. On the theoretical side, his work is rooted in probability theory and partial differential equations, with particular emphasis on stochastic processes and stochastic partial differential equations driven by generalized differential operators. He is especially interested in differential equations involving measure-theoretic and fractional operators, for which the associated solutions may exhibit jumps or singular behavior. His interests also encompass the general theory of stochastic processes, ranging from stationary processes to random fields, with direct and indirect connections to the theory of random measures and their analytical and probabilistic foundations.
On the applied side, Kelvin focuses on problems in mathematical statistics on complex domains, including Euclidean domains, metric graphs, and surface manifolds, with a strong emphasis on Bayesian modeling. A central theme of his applied research is the development of theoretical foundations for non-Gaussian latent models arising from fractional stochastic partial differential equations, such as Whittle–Matérn-type models. These developments are achieved through the use of tools from classical numerical analysis, including finite volume and lumped mass discretization methods, bridging rigorous analysis with scalable statistical inference for spatial and spatio-temporal data on complex geometries.
Education
- Doctor of Philosophy (Ph.D.)
- Mathematics, Federal University of Paraíba, Brazil, 2022
- Master of Science (M.S.)
- Mathematics, Federal University of Piauí, Brazil, 2018
- Bachelor of Science (B.S.)
- Mathematics, Federal University of the Delta of Parnaíba, Brazil, 2016
Quote
My research lies at the intersection of probability, partial differential equations, and statistics, with a focus on non-Gaussian stochastic models and their applications to complex spatial domains.
Selected Publications
- Simas, A. B., & Jhonson, K. (2025). One-sided Measure Theoretic Elliptic Operators and Applications to SDEs Driven by Gaussian White Noise with Atomic Intensity. Potential Analysis, 63, 34. Retrieved from https://link.springer.com/article/10.1007/s11118-025-10208-1 (Original work published 2025)
