Optimization of joint p-variations of Brownian semimartingales

Emmanuel Gobet (1) , Nicolas Landon (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We study the optimization of the joint $(p^Y,p^Z)-$variations of two continuous semimartingales $(Y,Z)$ driven by the same Itô process $X$. The $p$-variations are defined on random grids made of finitely many stopping times. We establish an explicit asymptotic lower bound for our criterion, valid in rather great generality on the grids, and we exhibit minimizing sequences of hitting time form. The asymptotics is such that the spatial increments of $X$ and the number of grid points are suitably converging to 0 and $+\infty$ respectively.

Mots clés: $p$-variation; almost-sure convergence; optimal stopping times

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Nicolas Landon. Optimization of joint p-variations of Brownian semimartingales. Electronic Communications in Probability, 2014, 19 (none), ⟨10.1214/ECP.v19-2975⟩. ⟨hal-00853590v2⟩