Covariation de convolution de martingales

Abstract

We evaluate the quadratic variation process in the sense of [5] and [6], which coincides with the classical quadratic variation in the case of semimartingales, for processes of the type {X t = ∫ 0 t G(t, s) dM(s), t ≥ 0}, where {G(t, s), t ≥ s ≥ 0} is a continuous deterministic function and M is a continuous square integrable martingale. Moreover, X admits an orthogonal representation. If G(t, s) = G (t − s), where G is a real function, then X coincides with a convolution of martingales.