Abstract
The Fractional Brownian Motion can be extended to complex values of the parameter $\alpha $ for $\Re\alpha \gt {1\over 2}$. 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 $\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 $\Re\alpha \le 1$, containing the classical case $\alpha =1$.
Citation
D. Feyel. A. de La Pradelle. "The FBM Itô's Formula Through Analytic Continuation." Electron. J. Probab. 6 1 - 22, 2001. https://doi.org/10.1214/EJP.v6-99
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