On Simpson’s Rule and Fractional Brownian Motion with $$H = 1/10$$ H = 1 / 10

Daniel Harnett () and David Nualart ()
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Daniel Harnett: University of Wisconsin-Stevens Point
David Nualart: University of Wisconsin-Stevens Point

Journal of Theoretical Probability, 2015, vol. 28, issue 4, 1651-1688

Abstract: Abstract We consider stochastic integration with respect to fractional Brownian motion (fBm) with $$H 1/10$$ H > 1 / 10 . For the case $$H = 1/10$$ H = 1 / 10 , we prove that the sequence of sums converges in distribution. Consequently, we have an Itô-like formula for the resulting stochastic integral. The convergence in distribution follows from a Malliavin calculus theorem that first appeared in Nourdin and Nualart (J Theor Probab 23:39–64, 2010).

Keywords: Itô formula; Skorohod integral; Malliavin calculus; Fractional Brownian motion; 60H05 (Primary); 60F05; 60G22; 60H07 (Secondary) (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10959-014-0552-1

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