Title: Learning Jump-Diffusion Dynamics from Irregularly-Sampled Data
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: generative modelling, irregular time series, jump processes, stochastic differential equations

Abstract: Accurately modeling time-continuous stochastic processes from irregular observations remains a significant challenge. In this paper, we leverage ideas from generative modeling of image data to push the boundary of time series generation. 
For this, we find new generators of SDEs and jump processes, inspired by trajectory flow matching, that have the marginal distributions of the time series of interest. 
Specifically, we can handle discontinuities of the underlying processes by parameterizing the jump kernel densities by scaled
Gaussians that allow for
closed form formulas and hence rapid evaluation of the corresponding
Kullback-Leibler divergence in the loss. 
Unlike most other approaches, we are able to handle irregularly sampled time series. We underline our theoretical results by numerical experiments involving combinations of jumps and SDE dynamics.