Project B08
Bayesian inference and mean field approximation for nonlinear (S)PDE

Project description

This project revisits Bayesian methods for complex problems like SDE/PDE parameter identification, focusing on stochastic and rough path systems. It aims to provide error guarantees for discretely observed multidimensional SDEs and McKean-Vlasov SDEs, define applicability using critical parameter dimension, develop Bayesian optimization-based solutions, and explore likelihood-based MCMC methods and error-in-operator problems in stochastic diffusions. 

Principal Investigators

Claudia Schillings (FU Berlin)

Vladimir Spokoiny (HU Berlin)

Sven Wang (EPFL)

Project members

Oleg Butkovsky (WIAS & HU Berlin)

Ilja Klebanov (FU Berlin)

Paolo Villani (FU Berlin)

Dana Wrischnig (FU Berlin)

Publications

• Athreya, S. & Butkovsky, O. Lê, K. & Mytnik, L. 2025. Analytically weak and mild solutions to stochastic heat equation with irregular drift. Stoch PDE: Anal Comp. https://doi.org/10.1007/s40072-025-00392-x

• Butkovsky, O., Dareiotis, K., Gerencsér, M., 2025. Strong rate of convergence of the Euler scheme for SDEs with irregular drift driven by Lévy noise. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, 61(4). https://doi.org/10.1214/24-AIHP1506

• Butkovsky, O., Lê, K., Mytnik, L., 2025. Stochastic equations with singular drift driven by fractional Brownian motion. Prob. Math. Phys. 6, 857–912. https://doi.org/10.2140/pmp.2025.6.857

Preprints

• Anzeletti, L., Butkovsky, O., Gerencsér, M., Shaposhnikov, A. 2025. Uniqueness for stochastic differential equations in Hilbert spaces with irregular drift. https://doi.org/10.48550/ARXIV.2512.25003

• Butkovsky, O. 2025. Lectures on stochastic sewing with applications. https://doi.org/10.48550/ARXIV.2510.12165