Rare events of small-noise Doob conditioned processes

Iago N. Mamede; Francesco Coghi

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arXiv · 2605.24537

Rare events of small-noise Doob conditioned processes

Iago N. Mamede·Francesco Coghi

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Abstract

Doob fixed-time conditioning enables the sampling of rare trajectories of Markov processes by modifying the drift so that reaching a prescribed target at a given time is guaranteed. We study the statistics of this conditioned path ensemble through the moment generating function in the weak-noise large deviation regime. Since the Doob drift is rarely available in closed form, we reinterpret the conditioned ensemble as the original process post-selected on the terminal constraint, thereby avoiding explicit construction of the Doob transform. This viewpoint then yields an optimal-control representation for the leading exponential contribution to the generating function, expressed as a variational principle with terminal boundary conditions set by the Doob end-point constraint. We illustrate the framework with two analytical examples and with an application to heat dissipation of a minimal model of biomolecular folding.

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Iago N. Mamede, Francesco Coghi. 2026-05-23. Rare events of small-noise Doob conditioned processes. https://arxiv.org/abs/2605.24537

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