A Stochastic Integral by a Near-Martingale

Hibino, Shinya; Kuo, Hui-Hsiung; Saitô, Kimiaki

doi:10.31390/cosa.12.2.07

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2021

2022

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“…The Itô isometry based on the new integral for anticipating processes was discussed by Kuo et al [17]. The near-martingale property of anticipating stochastic integral introduced in Kuo et al [16] have been recently studied in Hwang et al [10] and Hibino et al [7].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Integral for Non-Adapted Processes Related to Sub-Fractional Brownian Motion when $H>1/2$

Belhadj¹,

Kandouci²,

Bouchentouf³

2021

Bulletin of the Inst. of Math. Academia Sinica(N.S.)

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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 subfractional 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.

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Section: Introductionmentioning

confidence: 99%