CS26: Inference for Stochastic Equations

Organizer: Ciprian Tudor (University of Lille)

Parameter estimation for SDEs with Rosenblatt noise

Petr Čoupek

The talk is devoted to parameter identification for solutions to (possibly non-linear) SDEs driven by additive Rosenblatt process and singularity of the induced laws on the path space. We propose a joint estimator for the drift parameter, diffusion intensity, and Hurst index that can be computed from discrete-time observations with a bounded time horizon and we prove its strong consistency under in-fill asymptotics with a fixed time horizon. As a consequence of this strong consistency, singularity of measures generated by the solutions with different drifts is shown. This results in the invalidity of a Girsanov-type theorem for Rosenblatt processes. The talk is based on the recent article \([1]\).

Bibliography

\([1]\) Čoupek, P., Kříž, P., Maslowski, B. “Parameter estimation and singularity of laws on the path space for SDEs driven by Rosenblatt processes", Stochastic Processes and their Applications, vol. 179, 2025, art. no. 104499.

Statistical inference for semi-linear SPDEs using spatial information

Sascha Gaudlitz

We consider the Bayesian non-parametric estimation of the reaction term in a semi-linear parabolic SPDE. Posterior contraction rates are proven by making use of the spatial ergodicity of the SPDE while the time horizon is fixed. We additionally prove a non-parametric Bernstein- von Mises Theorem for the posterior distribution. The analysis of the posterior requires new concentration results for spatial averages of transformation of the SPDE, which are based the combination of the Clark-Ocone formula with bounds on the marginal densities.