Faculty of Mathematics and Computer Science
Department of Mathematics
BabeÅŸ-Bolyai University
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My main area of research is Stochastic Analysis. I focus on the analytical study of nonlinear stochastic partial differential equations (SPDEs), primarily SPDEs driven by transport noise which are used in ocean and climate modelling. I am strongly motivated by the challenge posed by randomness in multi-scale fluid dynamics and by the probabilistic descriptions that can be derived. In addition, I am interested in nonlinear filtering and high-dimensional data assimilation problems which involve SPDEs driven by different types of noise.
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I have obtained existence and uniqueness of solutions for several nonlinear stochastic transport models: the two-dimensional Euler equation, the great lake equation, two new stochastic rotating shallow water (SRSW) models with similar types of stochasticity, etc. I have also proven the applicability of one of these SRSW models in a data assimilation setting. I am currently working on Eulerian and pathwise calibration approaches for transport SPDEs, blow-up issues, and Hurst parameter estimation problems.
Fields of interest: Stochastic Partial Differential Equations, Probability Theory, Nonlinear Filtering & Data Assimilation, Statistical Aspects of Stochastic Fluid Dynamics.
Publications
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Published papers:
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1. Global solutions for stochastically controlled fluid dynamics models, Stoch PDE: Anal Comp(2025), DOI: 10.1007/s40072-025-00396-7, Q1 WOS (w. D. Crisan).
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2. Bayesian inference for geophysical fluid dynamics using generative models, Philosophical Transactions of the Royal Society A (2025), DOI: 10.1098/rsta.2024.0321, Q1 WOS (w. D. Crisan, A. Lobbe).
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3. Well-posedness for a stochastic 2D Euler equation with transport noise, Stoch PDE: Anal Comp, DOI:10.1007/s40072-021-00233-7, Q1 WOS (w. D. Crisan).
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4. Analytical Properties for a Stochastic Rotating Shallow Water Model Under Location Uncertainty, Journal of Mathematical Fluid Mechanics, DOI: 10.1007/s00021-023-00769-9, Q1 WOS (w. D. Crisan, E. Mémin).
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5. Well-posedness Properties for a Stochastic Rotating Shallow Water Model, J Dyn Diff Equat, DOI:10.1007/s10884-022-10243-1, Q2 WOS (w. D. Crisan).
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6. Well-posedness for the great lake equation with transport noise, Rev. Roumaine Math. Pures Appl. 66 (2021), 1, 131–155 (w. D. Crisan).
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7. Bayesian Inference for fluid dynamics: a case study for the stochastic rotating shallow water model, Frontiers in Applied Mathematics and Statistics, DOI: 10.3389/fams.2022.949354 (w. P. J. van Leeuwen, D. Crisan, R. Potthast).
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8. A pathwise parameterisation for stochastic transport, Stochastic Transport in Upper Ocean Dynamics (STUOD) Proceedings I (2023) by Springer Nature (w. Wei Pan).
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9. Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model, Stochastic & Dynamics, DOI: 10.1142/S02194937235003 (w. R. Mensah, D. Crisan, W. Pan, D. Holm).
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10. Existence and uniqueness of maximal solutions to SPDEs with applications to viscous fluid equations, Stochastics and Partial Differential Equations: Analysis and Computations, DOI: 10.1007/s40072-023-
00305-w, Q1 WOS (w. D. Goodair, D. Crisan).
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11. Noise calibration for SPDEs: A case study for the rotating shallow water model, Foundations of Data Science, DOI: 10.3934/fods.2023012 (w. A. Lobbe, D. Crisan, P. J. van Leeuwen, R. Potthast).
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12. Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models, Stochastic Transport in Upper Ocean Dynamics (STUOD) Proceedings II (2024) by Springer Nature (w. B. Chapron,
D. Crisan, D. Holm, A. Lobbe, E. Mémin).
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13. Generative modelling of stochastic rotating shallow water noise, in Stochastic Transport in Upper Ocean Dynamics (STUOD) Proceedings III (2025) by Springer Nature (w. D. Crisan, A. Lobbe).
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PhD Thesis:
O. Lang, Nonlinear stochastic transport partial differential equations: well-posedness and applications to data assimilation, PhD Thesis (2020), https://doi.org/10.25560/89816.
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