Fractional Brownian Motion Simulation: Observing Fractal Statistics in the Wild and Raising them in Captivity

On The Behavior of Malaysian Equities: Fractal Analysis Approach

Fractal analyzing of continuous processes have recently emerged in literatures in various domains. Existence of long memory in many processes including financial time series have been evidenced via different methodologies in many literatures in past decade, which has inspired many recent literatures on quantifying the fractional Brownian motion (fBm) characteristics of financial time series. Th...

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

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

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)...

On the usefulness of wavelet-based simulation of fractional Brownian motion∗†

We clarify some ways in which wavelet-based synthesis of fractional Brownian motion is used and can be useful. In particular, we examine the choice of an initial scale in the waveletbased synthesis method, compare it to other methods for simulation of fractional Brownian motion, and discuss connections to strong invariance principles encountered in Probability and Statistics.