2019/08/05 by Lassalle, Rémi
#FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1908.01641
In this paper, we investigate specific least action principles for laws of stochastic processes within a framework which stands on filtrations preserving variations. The associated Euler-Lagrange conditions, which we obtain, exhibit a deterministic process in the dynamics aside the canonical martingale term. In particular, taking specific action functionals, extremal processes with respect to those variations encompass specific laws of continuous semi-martingales whose drift characteristic is integrable with independent increments. Then, we relate extremal processes of classical cost functions, in particular of specific entropy functions, to a class of forward-backward systems of Mckean-Vlasov stochastic differential equations.