Covariation of martingales convolution

Mohammed Errami; Francesco Russo

doi:10.1016/S0764-4442(98)85014-3

Covariation of martingales convolution

Mohammed Errami
, Francesco Russo

Institut Galilée

Research output: Contribution to journal › Article › peer-review

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.

Translated title of the contribution	Covariation de convolution de martingales
Original language	English
Pages (from-to)	601-606
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	326
Issue number	5
DOIs	https://doi.org/10.1016/S0764-4442(98)85014-3
Publication status	Published - 1 Jan 1998
Externally published	Yes

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Covariation of martingales convolution

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