Feyel, D.; de La Pradelle, A. The fBm Itô’s formula through analytic continuation. (English) Zbl 1008.60074 Electron. J. Probab. 6, Paper No. 26, 22 p. (2001). Summary: The fractional Brownian motion (fBm) can be extended to complex values of the parameter \(\alpha \) for \(\operatorname {Re}\alpha >{1\over 2}\). This is a useful tool. Indeed, the obtained process depends holomorphically on the parameter, so that many formulas, as Itô formula, can be extended by analytic continuation. For large values of \(\operatorname {Re}\alpha \), the stochastic calculus reduces to a deterministic one, so that formulas are very easy to prove. Hence they hold by analytic continuation for \(\operatorname {Re}\alpha \leq 1\), containing the classical case \(\alpha =1\). Cited in 3 Documents MSC: 60H05 Stochastic integrals 60H07 Stochastic calculus of variations and the Malliavin calculus Keywords:Wiener space; Sobolev space; stochastic integral; fractional Brownian motion; Itô’s formula PDFBibTeX XMLCite \textit{D. Feyel} and \textit{A. de La Pradelle}, Electron. J. Probab. 6, Paper No. 26, 22 p. (2001; Zbl 1008.60074) Full Text: DOI EuDML EMIS