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.

Generation of Respiratory Flow Having Fractal Signal Feature

2011 ◽  
Vol 366 ◽  
pp. 211-214
Author(s):  
Zhong Hai He ◽  
Yi Hao Du ◽  
Zhao Xia Wu
Keyword(s):  
Life Support ◽  
Patient Simulation ◽  
Medical Patient ◽  
Heart Beat ◽  
Mechanical Ventilators ◽  
Patient Simulator ◽  
Physiological Signal ◽  
Respiratory Flow ◽  
Fractal Signal ◽  
Heart Beat Rate

In this paper how to generate respiratory flow that has fractal signal feature is introduced. Physiological signal have fractal feature have been verified by many researchers, such as heart beat rate, interbreath interval. Mechanical ventilators are used to provide life support for patients with respiratory failure. But these machines can damage the lung, causing them to collapse. On the other hand, fractal feature can be used as an indication of health situation; as a result in patient simulation the physiological signal should also have fractal features. The fractal feature is generated by fractional Brownian motion simulation. The fractal dimension is decided by Hurst exponent in routine. The algorithm is realized by R language and result is input into LabVIEW which have friendly interface and easy for simulation control usage. The method can be used in design of mechanical ventilator and medical patient simulator.

scholarly journals Least squares type estimations for discretely observed nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind

2021 ◽  
Vol 7 (1) ◽  
pp. 1095-1114
Author(s):  
Huantian Xie ◽  
◽  
Nenghui Kuang ◽  
Keyword(s):  
Brownian Motion ◽  
Least Squares ◽  
Fractional Brownian Motion ◽  
Unknown Parameter ◽  
Discrete Observations ◽  
Bifractional Brownian Motion ◽  
Similar Index ◽  
Self Similar ◽  
Strongly Consistent ◽  
Theoretical Results

<abstract><p>We consider the nonergodic Gaussian Ornstein-Uhlenbeck processes of the second kind defined by $ dX_t = \theta X_tdt+dY_t^{(1)}, t\geq 0, X_0 = 0 $ with an unknown parameter $ \theta &gt; 0, $ where $ dY_t^{(1)} = e^{-t}dG_{a_{t}} $ and $ \{G_t, t\geq 0\} $ is a mean zero Gaussian process with the self-similar index $ \gamma\in (\frac{1}{2}, 1) $ and $ a_t = \gamma e^{\frac{t}{\gamma}} $. Based on the discrete observations $ \{X_{t_i}:t_i = i\Delta_n, i = 0, 1, \cdots, n\} $, two least squares type estimators $ \hat{\theta}_n $ and $ \tilde{\theta}_n $ of $ \theta $ are constructed and proved to be strongly consistent and rate consistent. We apply our results to the cases such as fractional Brownian motion, sub-fractional Brownian motion, bifractional Brownian motion and sub-bifractional Brownian motion. Moreover, the numerical simulations confirm the theoretical results.</p></abstract>

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.

AN INTRODUCTION TO THE THEORY OF SELF-SIMILAR STOCHASTIC PROCESSES

2000 ◽  
Vol 14 (12n13) ◽  
pp. 1399-1420 ◽  
Author(s):  
PAUL EMBRECHTS ◽  
MAKOTO MAEJIMA
Keyword(s):  
Probability Theory ◽  
Brownian Motion ◽  
Stochastic Processes ◽  
Fractional Brownian Motion ◽  
High Energy Physics ◽  
High Energy ◽  
Point Of View ◽  
Long Range Dependence ◽  
Self Similar ◽  
Energy Physics

Self-similar processes such as fractional Brownian motion are stochastic processes that are invariant in distribution under suitable scaling of time and space. These processes can typically be used to model random phenomena with long-range dependence. Naturally, these processes are closely related to the notion of renormalization in statistical and high energy physics. They are also increasingly important in many other fields of application, as there are economics and finance. This paper starts with some basic aspects on self-similar processes and discusses several topics from the point of view of probability theory.

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.

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