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arXiv · 1712.08490

Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles

Francesco C. De Vecchi
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Abstract

Finite dimensional solutions to a class of stochastic partial differential equations are obtained extending the differential constraints method for deterministic PDE to the stochastic framework. A geometrical reformulation of the stochastic problem using the concept of infinite jet bundles is provided and a practical algorithm for explicitly computing these finite dimensional solutions is developed. This method, covering the majority of the current literature, is applied to a set of new SPDEs admitting finite dimensional solutions taken from Heath-Jarrow-Morton framework, stochastic hydrodynamics and filtering theory.

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Francesco C. De Vecchi. 2017-12-22. Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles. https://arxiv.org/abs/1712.08490

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