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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. 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 and preprints:
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Published papers:
1. Well-posedness for a stochastic 2D Euler equation with transport noise, Stoch PDE: Anal Comp, https://doi.org/10.1007/s40072-021-00233-7 (joint with D. Crisan).
2. Well-posednessfor the great lake equation with transport noise, Rev. Roumaine Math. Pures Appl. 66 (2021), 1, 131–155 (joint with D. Crisan).
3. Bayesian Inference for fluid dynamics: a case study for the stochastic rotating shallow water model, Frontiers in Applied Mathematics and Statistics, 8:949354, doi: 10.3389/fams.2022.949354 (joint with P. J. van Leeuwen, D. Crisan, R. Potthast).
4. A pathwise parameterisation for stochastic transport, STUOD Proceedings by Springer Nature (joint with Wei Pan).
5. Well-posedness Properties for a Stochastic Rotating Shallow Water Model, J Dyn Diff Equat (2023). https://doi.org/10.1007/s10884-022-10243-1 (joint with D. Crisan).
6. Analytical Properties for a Stochastic Rotating Shallow Water Model under Location Uncertainty, J. Math. Fluid Mech. 25, 29 (2023). https://doi.org/10.1007/s00021-023-00769-9 (joint with D. Crisan, E. Mémin).
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7. Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model, arXiv:2207.07457, to appear in Stochastics and Dynamics (joint with R. Mensah, D. Crisan, W. Pan, D. Holm).
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PhD Thesis:
O. Lang, Nonlinear stochastic transport partial differential equations: well-posedness and data assimilation, PhD Thesis (2020), https://doi.org/10.25560/89816.
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Preprints:
1. Existence and uniqueness of maximal solutions to SPDEs with applications to viscous fluid equations, arXiv:2209.09137v1, (joint with D. Goodair, D. Crisan).
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2. Comparison of Stochastic Parametrization Schemes using Data Assimilation on Triad Models, preprint (joint with A. Lobbe, D. Crisan, D. Holm, E. Mémin, B. Chapron).
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3. Noise calibration for the stochastic rotating shallow water model, preprint (joint with A. Lobbe, D. Crisan, P. J. van Leeuwen, R. Potthast).
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