Learning Ergodic Dynamical Systems from a Finite Trajectory
We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system. More precisely, we study discrete-time autonomous stochastic systems defining time-homogeneous Markov processes. We first focus on estimating the optimal one-step prediction function by nonlinear least squares, and derive high-probability guarantees measured with respect to the invariant measure of the process. These results make explicit how the non-independent and non-identically distributed nature of trajectory data modifies the classical statistical learning analysis. We then extend the framework to higher-order systems and finite-state spaces. Finally, we show that the same ...
| Authors | Oleksii Kachaiev, Silvia Villa, Lorenzo Rosasco |
|---|---|
| Primary category | stat.ML |
| Published | 24 July 2026 |
| Last updated at source | 24 July 2026 |
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