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arXiv · 2504.06411

On Stochastic Variational Principles

Archishman Saha
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Abstract

The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at deterministic endpoints, but also fixed at first entry times and first exit times for charts in a manifold. We prove a stochastic version of the fundamental lemma of calculus of variations in the context of these variations. Using this framework, we provide a generalization of the stochastic Hamilton-Pontryagin principle in local coordinates to arbitrary noise semimartingales. For the corresponding global form of the stochastic Hamilton-Pontryagin principle, we introduce a novel approach to global variational principles by restricting to semimartingales obtained as solutions of Stratonovich equations.

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Archishman Saha. 2025-04-08. On Stochastic Variational Principles. https://doi.org/10.1142/s297245892550008x

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