Extending self-similarity for fractional Brownian motion
نویسندگان
چکیده
منابع مشابه
Extending self-similarity for fractional Brownian motion
The fractional Brownian motion (fBm) model has proven to be valuable in modeling many natural processes because of its persistence for large time lags. However, the model is characterized by one single parameter that cannot distinguish between shortand long-term correlation effects. This work investigates the idea of extending selfsimilarity to create a correlation model that generalizes discre...
متن کاملRenormalized Self - Intersection Local Time for Fractional Brownian Motion
Let B H t be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1). Assume d ≥ 2. We prove that the renor-malized self-intersection local time ℓ = T 0 t 0 δ(B H t − B H s) ds dt − E T 0 t 0 δ(B H t − B H s) ds dt exists in L 2 if and only if H < 3/(2d), which generalizes the Varadhan renormalization theorem to any dimension and with any Hurst parameter. Motivated by a resul...
متن کاملLacunary Fractional Brownian Motion
In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.
متن کاملSelf-similarity and fractional Brownian motions on Lie groups
The goal of this paper is to define and study a notion of fractional Brownian motion on a Lie group. We define it as at the solution of a stochastic differential equation driven by a linear fractional Brownian motion. We show that this process has stationary increments and satisfies a local self-similar property. Furthermore the Lie groups for which this self-similar property is global are char...
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: IEEE Transactions on Signal Processing
سال: 1994
ISSN: 1053-587X
DOI: 10.1109/78.340789