Journal
BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES
Volume 16, Issue 4, Pages 321-337Publisher
ACAD SINICA
DOI: 10.21915/BIMAS.2021403
Keywords
Fractional Brownian motion; Levy-Hida representation; stochastic integration; Gaussian measure; Instantly independent processes
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In this paper, a new approach to stochastic integration of instantly independent stochastic processes with respect to fractional Brownian motion on a finite interval is proposed. The main focus is to discover the counterpart of the Ito theory, and some results on stochastic integration with respect to non-adapted processes are shown by generalizing previous results in the Brownian framework obtained by Ayed and Kuo.
In this paper, we propose a new approach to stochastic integration of the class of instantly independent stochastic processes with respect to fractional Brownian motion on a finite interval. The appraisal point is to discover the counterpart of the Ito theory. More precisely, we show some result on stochastic integration with respect to no adapted processes by generalizing the results obtained by Ayed and Kuo [5] in the Brownian framework.
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