Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles
Probability
2017-12-25 v1 Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1712.08490,
title = {Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles},
author = {Francesco C. De Vecchi},
journal= {arXiv preprint arXiv:1712.08490},
year = {2017}
}