Stochastic diffusions are widely used to model physical phenomena, with noise playing a key role in capturing average effects that do not need to be explicitly defined. However, the proposed model is always an approximation and cannot exactly reproduce all aspects of the real system (such as the mean, variance, or higher-order moments). When a discrepancy between the model and the real system is observed, it is natural to refine the model to better account for this difference.
Based on the Gibbs conditioning principle, this talk presents a systematic approach to constrain the distribution of a diffusion process at each time point. A thorough regularity analysis is performed on the corrected process, and quantitative stability is explored by perturbing the constraints, demonstrating the robustness of the correction procedure. This work is a collaboration with Giovanni Conforti and Julien Reygner.