Integration with Respect to Fractional Local times with Hurst Index
نویسندگان
چکیده
In this paper, we study the stochastic integration with respect to local times of fractional Brownian motion B with Hurst index 1/2 < H < 1. As a related problem we define the weighted quadratic covariation [f(B), B ] ) of f(B) and B as follows n−1
منابع مشابه
ar X iv : 0 80 3 . 36 65 v 2 [ m at h . PR ] 4 D ec 2 00 8 INTEGRATION WITH RESPECT TO FRACTIONAL LOCAL TIME WITH HURST INDEX
Let L (x, t) = 2H R t 0 δ(B s − x)s ds be the weighted local time of fractional Brownian motion B with Hurst index 1/2 < H < 1. In this paper, we use Young integration to study the integral of determinate functions R R f(x)L (dx, t). As an application, we investigate the weighted quadratic covariation [f(B), B ] ) defined by [f(B), B ] (W ) t := lim n→∞ 2H n−1
متن کاملRegularity of Intersection Local Times of Fractional Brownian Motions
Let Bi be an (Ni, d)-fractional Brownian motion with Hurst index αi (i = 1,2), and let B1 and B2 be independent. We prove that, if N1 α1 + N2 α2 > d , then the intersection local times of B1 and B2 exist, and have a continuous version. We also establish Hölder conditions for the intersection local times and determine the Hausdorff and packing dimensions of the sets of intersection times and int...
متن کاملA Note on the Clark-Ocone Theorem for Fractional Brownian Motions with Hurst Parameter bigger than a Half
Integration with respect to a fractional Brownian motion with Hurst parameter 1/2 < H < 1 is related to the inner product: (f, g)H = H(2H − 1) ∫
متن کاملStochastic integration with respect to the fractional Brownian motion
We develop a stochastic calculus for the fractional Brownian motion with Hurst parameter H > 2 using the techniques of the Malliavin calclulus. We establish estimates in Lp, maximal inequalities and a continuity criterion for the stochastic integral. Finally, we derive an Itô’s formula for integral processes.
متن کامل9 Are fractional Brownian motions predictable ?
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. 1 Intoduction The question in the title is provocative, of course. Everybody familiar with the theory of stochast...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008