scholarly journals Simulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion

2021 ◽  
pp. 11-19
Author(s):  
O. I. Vasylyk ◽  
I. I. Lovytska
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Series Representation ◽  
Random Processes ◽  
Specific Class ◽  
Programming Environment ◽  
Motion Simulation ◽  
Actuarial Mathematics ◽  
R Programming ◽  
Simulation Parameters

In the paper, we consider the problem of simulation of a strictly φ-sub-Gaussian generalized fractional Brownian motion. Simulation of random processes and fields is used in many areas of natural and social sciences. A special place is occupied by methods of simulation of the Wiener process and fractional Brownian motion, as these processes are widely used in financial and actuarial mathematics, queueing theory etc. We study some specific class of processes of generalized fractional Brownian motion and derive conditions, under which the model based on a series representation approximates a strictly φ-sub-Gaussian generalized fractional Brownian motion with given reliability and accuracy in the space C([0; 1]) in the case, when φ(x) = (|x|^p)/p, |x| ≥ 1, p > 1. In order to obtain these results, we use some results from the theory of φ-sub-Gaussian random processes. Necessary simulation parameters are calculated and models of sample pathes of corresponding processes are constructed for various values of the Hurst parameter H and for given reliability and accuracy using the R programming environment.

Generate Breath Flow Having Fractal Signal Feature Using Weierstrass Function Combination

2011 ◽  
Vol 393-395 ◽  
pp. 796-799
Author(s):  
Meng Chao Li ◽  
Zhong Hai He
Keyword(s):  
Mechanical Ventilation ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Medical Patient ◽  
Motion Simulation ◽  
Weierstrass Function ◽  
Patient Simulator ◽  
Function Combination ◽  
Fractal Signal ◽  
Self Similar

Fractal signal feature in breath flow is verified by many articles. So the generate fractal feature have two meanings, one to decrease damage to lung in mechanical ventilation because of natural similar, two to increase similarity in breath simulation used in medical patient simulator. The main feature of fractal signal is self-similar. Some algorithms have been proposed using fractional Brownian motion simulation. In this paper we use Weierstrass function combination to generate fractal signal. The method includes all fractal features and easy to realize in algorithm compared with fractional Brownian motion.

ENGINEERING APPLICATIONS OF FRACTIONAL BROWNIAN MOTION: SELF-AFFINE AND SELF-SIMILAR RANDOM PROCESSES

Fractals ◽  
1999 ◽  
Vol 07 (02) ◽  
pp. 151-157 ◽  
Author(s):  
P. S. ADDISON ◽  
A. S. NDUMU
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Random Processes ◽  
The Other ◽  
Engineering Applications ◽  
Self Similar ◽  
Diffusive Processes ◽  
Spatial Trajectories

The purpose of this paper is to explain the connection between fractional Brownian motion (fBm) and non-Fickian diffusive processes, and at the same time, highlight three engineering applications: two requiring self-affine fBm trace functions and the other requiring self-similar fBm spatial trajectories.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

Global attracting sets of neutral stochastic functional integro-differential equations driven by a fractional Brownian motion

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Bakka ◽  
S. Hajji ◽  
D. Kiouach
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Brownian Motion ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Hurst Parameter ◽  
Fixed Point Principle ◽  
Stochastic Functional

Abstract By means of the Banach fixed point principle, we establish some sufficient conditions ensuring the existence of the global attracting sets of neutral stochastic functional integrodifferential equations with finite delay driven by a fractional Brownian motion (fBm) with Hurst parameter H ∈ ( 1 2 , 1 ) {H\in(\frac{1}{2},1)} in a Hilbert space.

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