Drift Estimation for Stochastic Reaction-Diffusion Systems

Speaker:

Gregory Pasemann, TU Berlin

Description:

In this talk we consider drift estimation for Stochastic Partial Differential Equations (SPDEs). While Girsanov's theorem implies that the drift of a finite dimensional stochastic differential equation cannot be determined in finite time, the situation changes drastically in the case of SPDEs with unbounded drift: The measures on path space induced by processes with different drift terms can become singular. This has first been observed in the seminal paper [2] for linear SPDEs, and [1] pioneered in extending these result to nonlinear dynamics, namely the two-dimensional Navier-Stokes equations. In this work [3] we generalize these results to abstract semilinear evolution equations. This covers models with considerably different dynamical behavior, such as phase field models, traveling wave dynamics or Burgers' equation. Further, we discuss robustness of the statistical procedure to model misspecification.

This is joint work with Wilhelm Stannat (TU Berlin).

References

[1] I. Cialenco, N. Glatt-Holtz, Parameter Estimation for the Stochastically Perturbed Navier-Stokes Equations, Stochastic Process. Appl. 121 (2011),

no. 4, 701-724.

[2] M. Hubner, R. Khasminskii, B. L. Rozovskii, Two Examples of Parameter Estimation for Stochastic Partial Differential Equations, Stochastic Processes (S. Cambanis, J. K. Ghosh, R. L. Karandikar, and P. K. Sen,

eds.), Springer, New York, 1993, pp. 149-160.

[3] G. Pasemann, W. Stannat, Drift Estimation for Stochastic Reaction-Diffusion Systems, arXiv:1904.04774, accepted for publication in Electronic Journal of Statistics, 2019+.

Topic:

Stochastic Analysis