I am searching for a reference for the law of iterated logarithm for the fractional Brownian motion.

As seen here a LIL for the fBM is given, but the author of the answer is not sure about the form of that $\limsup$; nevertheless he gives a reference (the Lifshits book). I searched in it profusely. I found a functional law of the IL, but it seems working only on the standard BM.

Then I tried to search following the author of the LIL for fBM: Oodaira, without finding anything.

Finally I searched on the web, but -and this sounds quite strange!- without any significant result.

Can someone give me a precise reference in which one can find the statement (and possibly, but not necessarily,the proof) of the law of the iterated logarithm for the fractional Brownian motion?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.