Weak calculus of variations for functionals of laws of semi-martingales
Probability
2015-01-22 v1 Optimization and Control
Abstract
We develop a non-anticipating calculus of variations for functionals on a space of laws of continuous semi-martingales, which extends the classical one. We extend Hamilton's least action principle and Noether's theorem to this generalized stochastic framework. As an application we obtain, under mild conditions, a stochastic Euler-Lagrange condition and invariants for the critical points of recent problems in stochastic control, namely for the semi-martingale optimal transportation problems.
Keywords
Cite
@article{arxiv.1501.05134,
title = {Weak calculus of variations for functionals of laws of semi-martingales},
author = {Ana Bela Cruzeiro and Rémi Lassalle},
journal= {arXiv preprint arXiv:1501.05134},
year = {2015}
}