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arXiv · 1208.5529

Noether's Theorem in the Stochastic Calculus of Variations

Adilson C. M. Barros·Delfim F. M. Torres
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Abstract

We begin by presenting the classical deterministic problems of the calculus of variations, with emphasis on the necessary optimality conditions of Euler-Lagrange and the Noether theorem. As examples of application, we obtain the conservation laws of momentum and energy from mechanics, valid along the Euler-Lagrange extremals. We then introduce the stochastic calculus of variations, proving a recent stochastic Noether-type theorem obtained by Cresson. We end by pointing out an interesting open problem.

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Adilson C. M. Barros, Delfim F. M. Torres. 2012-08-27. Noether's Theorem in the Stochastic Calculus of Variations. https://arxiv.org/abs/1208.5529

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