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Stochastic integration with respect to fractional Brownian motion defined by non-uniform Riemann. (Chinese. English summary) Zbl 1164.60413

Summary: The stochastic integral with respect to a fractional Brownian motion is defined by the non-uniform Riemann approach. The link between the integral \(\int^L_0u (s)\,dB^H (s)= (-1)^\alpha\int^L_0D^\alpha_{0+}u_{0+} (s)D^{1-\alpha}_{L-}B^H_{L-} (s)\,ds+u (0+)B^H_L\) and the stochastic integral is established in this paper.

MSC:

60J65 Brownian motion
60H05 Stochastic integrals
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