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Stochastic Integral for Non-Adapted Processes Related to Sub-Fractional Brownian Motion when $H>1/2$
by Amel Belhadj   Abdeldjebbar Kandouci   Amina Angelika Bouchentouf

Vol. 16 No. 2 (2021) P.165~P.176
 DOI: https://doi.org/10.21915/BIMAS.2021203 10.21915/BIMAS.2021203

ABSTRACT

In this paper, we define the stochastic integral of an anticipating integrand, which is a product of instantly independent process and adapted process, with respect to sub-fractional Brownian motion based on Ayed and Kuo's approach. This provides a new concept of stochastic integration of non-adapted process. Further, we prove that our anticipating integral is a near-martingale under some conditions.

KEYWORDS
Stochastic integral, sub-fractional Brownian motion, non-adapted process, near martingale.

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 60H05, 60G15.

MILESTONES