Collective Online Clicking Pattern on BBS as Geometric Brown Motion

In this paper, the Brown motion PSO is proposed to deal with the slow convergence, low precision and local optimal problem of the Particle Swarm Optimization (PSO) algorithm in solving the complex functions. The wave operator is designed, which is similar to the differential mutation operator, to improve the particle velocity formula. The new algorithm is applied in the design of the adaptive filter; Experiments results show that the new algorithm has the faster convergence than the traditional PSO algorithm, and it has the better stability.

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Local times for the norm of a multidimensional Brown motion

Journal of Soviet Mathematics ◽

10.1007/bf01362811 ◽

1992 ◽

Vol 61 (1) ◽

pp. 1947-1949

Author(s):

V. A. Shakh

Keyword(s):

Local Times ◽

Brown Motion

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Application of G-Brown Motion in the Stock Price

Journal of Mathematical Finance ◽

10.4236/jmf.2020.101003 ◽

2020 ◽

Vol 10 (01) ◽

pp. 27-34

Author(s):

Chuankang Chai

Keyword(s):

Stock Price ◽

Brown Motion

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A Stochastic SIS Epidemic Model with Ornstein-Uhlenbeck Process and Brown Motion

10.21203/rs.3.rs-679213/v1 ◽

2021 ◽

Author(s):

Xingzhi Chen ◽

Baodan Tian ◽

Xin Xu ◽

Ruoxi Yang ◽

Shouming Zhong

Keyword(s):

Basic Reproduction Number ◽

Epidemic Model ◽

Reproduction Number ◽

Global Solutions ◽

Uhlenbeck Process ◽

Sis Epidemic Model ◽

Ornstein Uhlenbeck Process ◽

Brown Motion ◽

Sis Epidemic ◽

The Basic Reproduction Number

Abstract This paper studies a stochastic differential equation SIS epidemic model, disturbed randomly by the mean-reverting Ornstein-Uhlenbeck process and Brownian motion. We prove the existence and uniqueness of the positive global solutions of the model and obtain the controlling conditions for the extinction and persistence of the disease. The results show that when the basic reproduction number Rs0 < 1, the disease will extinct, on the contrary, when the basic reproduction number Rs0 > 1, the disease will persist. Furthermore, we can inhibit the outbreak of the disease by increasing the intensity of volatility or decreasing the speed of reversion ϑ, respectively. Finally, we give some numerical examples to verify these results.

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Applications of Micro-PIV Technique in Visualization of Flow in Microspace

First International Conference on Integration and Commercialization of Micro and Nanosystems, Parts A and B ◽

10.1115/mnc2007-21434 ◽

2007 ◽

Author(s):

Ruijin Wang ◽

Jianzhong Lin ◽

Yifeng Wang

Keyword(s):

Cross Correlation ◽

Particle Image ◽

Characteristic Length ◽

Tracer Particle ◽

Image Process ◽

Micro Piv ◽

Correlation Algorithm ◽

Piv Technique ◽

Image Velocimetry ◽

Brown Motion

A micro-resolution particle image velocimetry (micro-PIV) technique for flow visualization in microspace is presented here. The micro-PIV system was constructed through adding an epi-fluorescence microscope, improving the light source and choosing suitable tracing particle. According to smaller characteristic length of the flow in microscale and higher precision prolepsis, an image process technique based on cross correlation algorithm was conducted. To eliminate the main error caused by Brown motion of tracer particle, an approach by averaging the velocities of the ensemble particles in same interrogation plot was brought forward. Micro-PIV measure-ments of three typical flows (in a micromixer, near barriers and in a micro-jet) were carried out. The experimental results show that the micro-PIV system is suitable to both steady and unsteady flow in microscale. It is helpful to design micro-devices and analysis on data collected from such micro-devices.

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