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The FBM Itô's Formula Through Analytic Continuation

   
@article{EJP99,
	author = {D. Feyel and A. de La Pradelle},
	title = {The FBM Itô's Formula Through Analytic Continuation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {6},
	year = {2001},
	keywords = {Wiener space, Sobolev space, Stochastic integral, FractionalBrownian Motion, Itô's formula.},
	abstract = {The Fractional Brownian Motion can be extended to complex values of the parameter $\alpha $ for $\Re\alpha >{1\over 2}$. 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 $\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 $\alpha =1$.},
	pages = {no. 26, 1-22},
	issn = {1083-6489},
	doi = {10.1214/EJP.v6-99},    
        url = {http://ejp.ejpecp.org/article/view/99}}