Title: Noise-to-Process Transformation: A Weak-Prior Paradigm for Single-Trajectory Stochastic Process Modeling
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Stochastic Processes; Weak-Prior Modeling;

Abstract: Stochastic processes offer a principled framework for trajectory-level uncertainty modeling from limited observations. Prior-driven methods (e.g., Gaussian processes) remain viable with scarce data but hinge on strong structural priors, whereas data-driven meta-approaches learn flexible representations yet typically require multi-trajectory supervision. To achieve flexibility from a single trajectory without strong priors, we introduce a noise-to-process (N2P) paradigm: a shared base-noise process \(Z\) is pushed through a single measurable generator $G_\theta$ to produce a full trajectory $X=G_\theta(Z)$, making projective consistency intrinsic by design. Instantiating the paradigm, we propose Deconvolution-Based Process Transformation (DBPT), a deconvolution-based generator that captures long-range, inter-temporal dependence. Across synthetic and diverse real single-trajectory tasks, DBPT delivers flexible uncertainty modeling and competitive performance to prior- and data-driven baselines.

TL;DR: This study introduces a noise-to-process transformation paradigm for weak-prior stochastic process modeling from single-trajectory.