Short Communications

On the sum of Gaussian martingale and an independent fractional Brownian motion

R. Belfadli^a, M. Chadad^b, M. Erraoui<sup>c

a</sup> Department of Mathematics, Faculty of Sciences and Technology, Cadi Ayyad University, Marrakech, Morocco
^b Mathematics Department, Faculty of Sciences Semalalia, Cadi Ayyad University, Marrakesh, Morocco
^c Mathematics Department, Faculty of Sciences, Chouaib Doukkali University, El Jadida, Morocco

Abstract: In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913–934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter $H \in (0,1)$. At the same time, we emphasize that the Markov property is lost even if the martingale owns it.

Keywords: Gaussian martingale, quasimartingale, semimartingale, entropy, equivalent measure, Markov process.

Received: 18.12.2020
Revised: 25.05.2022
Accepted: 20.09.2022

DOI: 10.4213/tvp5466

 English version: Theory of Probability and its Applications, 2023, 68:2, 316–323

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