Power variation of multiple fractional integrals
Constantin Tudor, Maria Tudor (2007)
Open Mathematics
Similarity:
Constantin Tudor, Maria Tudor (2007)
Open Mathematics
Similarity:
David Nualart, Aurel Rascanu (2002)
Collectanea Mathematica
Similarity:
A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
Bojdecki, Tomasz, Gorostiza, Luis G., Talarczyk, Anna (2007)
Electronic Communications in Probability [electronic only]
Similarity:
Dai, W., Heyde, C.C. (1996)
Journal of Applied Mathematics and Stochastic Analysis
Similarity:
Cheridito, Patrick, Kawaguchi, Hideyuki, Maejima, Makoto (2003)
Electronic Journal of Probability [electronic only]
Similarity:
David Nualart (2006)
Annales de la faculté des sciences de Toulouse Mathématiques
Similarity:
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter called the Hurst index. In this conference we will survey some recent advances in the stochastic calculus with respect to fBm. In the particular case , the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô calculus cannot be used. Different approaches have been introduced to construct stochastic integrals with...
Kleptsyna, M.L., Kloeden, P.E., Anh, V.V. (1999)
Journal of Applied Mathematics and Stochastic Analysis
Similarity:
Charles El-Nouty (2007)
ESAIM: Probability and Statistics
Similarity:
We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.
Lanjri Zadi, Noureddine, Nualart, David (2003)
Electronic Communications in Probability [electronic only]
Similarity:
Boufoussi, Brahim, Ouknine, Youssef (2003)
Electronic Communications in Probability [electronic only]
Similarity: