Fractional Brownian motion as a nonstationary process: An alternative paradigm for DNA sequences

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Affine stationary processes with applications to fractional Brownian motion

ABSTIUCT In our previous work, we introduced a new class of nonstationary stochastic processes whose spectral representation is associated with the wavelet transforms and established a mathematical framework for the analysis of such processes 111. We refer to these processes as uffine stptionary processes. These processes are indexed by the affine p u p , or ax+b group, which can be though of a...

An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions

Fluid flow and solute transport in the subsurface are known to be strongly influenced by the heterogeneity of aquifers. To simulate aquifer properties, such as logarithmic hydraulic conductivity (lnðKÞ) variations, fractional Brownian motion (fBm) and truncated fractional Levy motion (fLm) were suggested previously. In this paper, an efficient three-dimensional successive random additions (SRA)...

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On the wavelet transform of fractional Brownian motion

The wavelet transform of a function f(t) is deened by the formula: Wf(t; a) = W a f(t) = 1 p a Z f(s)g(t ? s a) ds where g(t) is a xed function, t 2 R and a 2 R +. This transform yields a joint timescale representation the original input function that has been of great recent interest. (See for example D1] D2] and HW]). In a recent correspondence, Flandrin F] proposed the use of the wavelet tra...