Brownian and fractional Brownian stochastic currents via Malliavin calculus
نویسندگان
چکیده
منابع مشابه
Brownian and fractional Brownian stochastic currents via Malliavin calculus
By using Malliavin calculus and multiple Wiener-Itô integrals, we study the existence and the regularity of stochastic currents defined as Skorohod (divergence) integrals with respect to the Brownian motion and to the fractional Brownian motion. We consider also the multidimensional multiparameter case and we compare the regularity of the current as a distribution in negative Sobolev spaces wit...
متن کاملVariations of the fractional Brownian motion via Malliavin calculus
Using recent criteria for the convergence of sequences of multiple stochastic integrals based on the Malliavin calculus, we analyze the asymptotic behavior of quadratic variations for the fractional Brownian motion (fBm) and we apply our results to the design of a strongly consistent statistical estimators for the fBms self-similarity parameter H. 2000 AMS Classi cation Numbers: 60F05, 60H05, ...
متن کاملFractional Brownian motion: stochastic calculus and applications
Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) called the Hurst index. In this note we will survey some facts about the stochastic calculus with respect to fBm using a pathwise approach and the techniques of the Malliavin calculus. Some applications in turbulence and finance will be discussed. Math...
متن کاملBrownian Motion and Stochastic Calculus
This note is about Doob decomposition and the basics of Square integrable martingales Contents 1 Doob-Meyer Decomposition 1 2 Square Integrable Martingales 4 Brownian Motion and Stochastic Calculus Continuout Time Submartingales Usually its su¢ ce to only discuss submartingales by symmetry in de nition and techniques are the same. 1 Doob-Meyer Decomposition Doob-meyer decomposition clears the ...
متن کاملStochastic calculus with respect to fractional Brownian motion
— Fractional Brownian motion (fBm) is a centered selfsimilar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) 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 H = 1/2, the process is an ordinary Brownian motion, but otherwise it is not a semimartingale and Itô...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2009.05.001