RESEARCH INTERESTS

I'm currently working on stochastic (partial) differential equations (S(P)DEs) and am particularly interested in processes driven by random martingale measures. My most recent project focused on establishing analytical properties for conditional densities of partially observed jump diffusion processes.

I also recently got interested in rough path theory and the fascinating new tools it provides. In a current project we try to use these to obtain an approximation for the prediction density, associated to the conditional expectation of a future state.

Apart from probability and stochastics I'm also interested in estimation for (nonlinear) infinite-dimensional systems. In my Master's project we derived an observer for a class of semilinear infinite-dimensional systems, based on the extended Kalman filter.

RESEARCH

Papers and preprints

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