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RESEARCH INTERESTS

II have projects in several domains of interest.

Regularity for evolution equations:

With Mark Veraar I work on SPDEs in an abstract / evolution equation setting. We look at variational methods in obtaining optimal regularity for SPDEs driven by random martingale measures.

Singular SPDEs:

In a joint project with Xue-Mei Li we investigate the well-posedness of singular parabolic SPDEs.

Applications and theory of Filtering:

In my PhD, under Istvàn Gyöngy, I worked on the regularity of the filtering density for partially observed jump-diffusions. 

In a collaboration with Marc Vidales (Uni Edinburgh) we applied signature methods to machine learning in filtering.

We are still working on extensions of our results in both theory and applications.

Regularization by noise: 

In a joint work with Helena Kremp (TU Wien) we prove well-posedness of Lévy SDEs with weak coefficients.

Another collaboration with Abdulwahab Mohamed (Uni Edinburgh) focuses on regularization by noise for evolution equations.

Apart from probability and stochastics I'm also interested in estimation for (nonlinear) infinite-dimensional systems. Following my Master's project, with Kirsten Morris (Uni Waterloo) we derived an observer for a class of semi-linear distributed parameter systems, based on the extended Kalman filter. We also obtained numerical results, which we applied to simulations of drug delivery systems.

RESEARCH

Papers and preprints.
For preprints of recent / unpublished projects please reach out.

with I. Gyongy

On partially observed jump diffusions III. Regularity of the filtering density,

arXiv:2211.07239

with I. Gyongy

On partially observed jump diffusions II. The filtering density,

arXiv:2205.14534

with I. Gyongy

On partially observed jump diffusions I. The filtering equations,

arXiv:2205.08286

with M. Sabate-Vidales

Learning the conditional law: signatures and conditional GANs in filtering and prediction of diffusion processes.,

arXiv:2204.00611, submitted to 61st IEEE Conference on Decicion and Control 2022

with S. Afshar and K. Morris

Extended Kalman filter based observer design for semilinear infinite-dimensional systems, (2022)

arXiv:2202.07797

with S. Afshar and K. Morris

Well-posedness of Extended Kalman Filter equations for semilinear infinite-dimensional systems,

59th IEEE Conference on Decision and Control (CDC), 2020, pp. 1210-1215,

doi: 10.1109/CDC42340.2020.9303759.

Doctoral Dissertation

On conditional densities of partially observed jump diffusions (2022)

Link to thesis

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