Abbreviated Journal Title
Electron. J. Probab.
Stochastic integration; Stratonovich integral; fractional Brownian; motion; weak convergence; Malliavin calculus; WEIGHTED QUADRATIC VARIATIONS; LIMIT-THEOREMS; CALCULUS; FORMULA; Statistics & Probability
Let B be a fractional Brownian motion with Hurst parameter H = 1 = 6. It is known that the symmetric Stratonovich-style Riemann sums for integral g (B(s)) dB (s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of cadlag functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary It integral with respect to a Brownian motion that is independent of B.
Electronic Journal of Probability
Nourdin, Ivan; Réveillac, Anthony; and Swanson, Jason, "The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6" (2010). Faculty Bibliography 2010s. 598.