Continuous time random walk with jump length correlated with waiting time

2013 ◽  
Vol 392 (4) ◽  
pp. 612-617 ◽  
Author(s):  
Jian Liu ◽  
Jing-Dong Bao
Keyword(s):  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Continuous Time Random Walk ◽  
Jump Length

A mathematical model for preventing HIV virus from proliferating inside CD4 T brownian cell using Gaussian jump nanorobot

2019 ◽  
Vol 12 (07) ◽  
pp. 1950076 ◽  
Author(s):  
Mohamed Abd Allah El-Hadidy ◽  
Alaa A. Alzulaibani
Keyword(s):  
Mathematical Model ◽  
Random Walk ◽  
Probability Density Function ◽  
Waiting Time ◽  
Continuous Time ◽  
Nonlinear Flow ◽  
Stat Phys ◽  
Jump Length ◽  
Hiv Virus ◽  
Probability Density Function Pdf

We present a statistical distribution of a nanorobot motion inside the blood. This distribution is like the distribution of A and B particles in continuous time random walk scheme inside the fluid reactive anomalous transport with stochastic waiting time depending on the Gaussian distribution and a Gaussian jump length which is detailed in Zhang and Li [J. Stat. Phys., Published Online with https://doi.org/10.1007/s10955-018-2185-8 , 2018]. Rather than estimating the length parameter of the jumping distance of the nanorobot, we normalize the Probability Density Function (PDF) and present some reliability properties for this distribution. In addition, we discuss the truncated version of this distribution and its statistical properties, and estimate its length parameter. We use the estimated distance to study the conditions that give a finite expected value of the first meeting time between this nanorobot in the case of nonlinear flow with independent [Formula: see text]-dimensional Gaussian jumps and an independent [Formula: see text]-dimensional CD4 T Brownian cell in the blood ([Formula: see text]-space) to prevent the HIV virus from proliferating within this cell.

scholarly journals A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Long Shi ◽  
Zuguo Yu ◽  
Zhi Mao ◽  
Aiguo Xiao
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Laplace Transform ◽  
Probability Density ◽  
Density Function ◽  
Waiting Time ◽  
Continuous Time ◽  
Dimensional Space ◽  
Continuous Time Random Walk ◽  
Random Walk Model

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density functionP(x,t)of finding the walker at positionxat timetis completely determined by the Laplace transform of the probability density functionφ(t)of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.

Sign in / Sign up

Export Citation Format

Share Document