Average preserving variation processes in view of optimization

Lassalle, Rémi

Published 2019-08-05Version 1

In this paper, within the specific framework of an intrinsic calculus of variations on laws of semi-martingales, which is based on information flows preserving perturbations, we investigate least action principles associated to average preserving variation processes. The associated Euler-Lagrange conditions, which we obtain, exhibit a deterministic process aside the canonical martingale term. In particular, taking specific action functionals, we have that critical processes with respect to those variations encompass specific laws of continuous semi-martingales whose drift characteristic is integrable with independent increments. Then, we relate critical processes of classical cost functions to a specific class of forward-backward systems.