Path Properties of a Generalized Fractional Brownian Motion
نویسندگان
چکیده
The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of shot noise with power-law shape function and non-stationary noises variance function. In this paper, we study sample path properties motion, including Hölder continuity, differentiability/non-differentiability, functional local law iterated logarithms.
منابع مشابه
Dimensional Properties of Fractional Brownian Motion
Let B = {Bα(t), t ∈ RN} be an (N, d)-fractional Brownian motion with Hurst index α ∈ (0, 1). By applying the strong local nondeterminism of B, we prove certain forms of uniform Hausdorff dimension results for the images of B when N > αd. Our results extend those of Kaufman [7] for one-dimensional Brownian motion. Running head: Dimensional Properties of Fractional Brownian Motion 2000 AMS Classi...
متن کاملSample Path Properties of Bifractional Brownian Motion
Let B = { B(t), t ∈ R+ } be a bifractional Brownian motion in R. We prove that B is strongly locally nondeterministic. Applying this property and a stochastic integral representation of B , we establish Chung’s law of the iterated logarithm for B , as well as sharp Hölder conditions and tail probability estimates for the local times of B . We also consider the existence and the regularity of th...
متن کاملSome Path Properties of Iterated Brownian Motion
We will consider the process {Z(t) df = X(Y (t)), t ≥ 0} which we will call “iterated Brownian motion” or simply IBM. Funaki (1979) proved that a similar process is related to “squared Laplacian.” Krylov (1960) and Hochberg (1978) considered finitely additive signed measures on the path space corresponding to squared Laplacian (there exists a genuine probabilistic approach, see, e.g., Ma̧drecki ...
متن کاملSome singular sample path properties of a multiparameter fractional Brownian motion
We prove a Chung-type law of the iterated logarithm for a multiparameter extension of the fractional Brownian motion which is not increment stationary. This multiparameter fractional Brownian motion behaves very differently at the origin and away from the axes, which also appears in the Hausdorff dimension of its range and in the measure of its pointwise Hölder exponents. A functional version o...
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 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 Theoretical Probability
سال: 2021
ISSN: ['1572-9230', '0894-9840']
DOI: https://doi.org/10.1007/s10959-020-01066-1