Direct Estimation of Schrödinger Bridge Time-Series Drifts: Finite-Sample, Asymptotic, and Adaptive Guarantees
We study nonparametric estimation of Schrödinger bridge (SB) drifts from i.i.d.\ data observed on a single time interval. Starting from the conditional-ratio form of the Schrödinger bridge time-series (SBTS) drift formula, we analyze a direct Nadaraya--Watson plug-in estimator built from kernelized numerator and denominator terms. Unlike recent SB analyses based on entropic-OT potentials, Sinkhorn iterations, or iterative bridge solvers, our approach works directly at the drift level and isolates \emph{statistical error} from optimization, approximation, and discretization error. Under Hölder regularity, a marginal-density floor, and bounded support, we prove a uniform non-asymptotic boun...
| Authors | Othmane Mazhar, Huyên Pham |
|---|---|
| Primary category | math.ST |
| Published | 6 May 2026 |
| Last updated at source | 6 May 2026 |
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