Continuous-time random walk: exact solutions for the probability density function and first two moments

2011 ◽  
Vol 84 (4) ◽  
pp. 045022 ◽  
Author(s):  
Kwok Sau Fa ◽  
Joni Fat
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Exact Solutions ◽  
Probability Density ◽  
Density Function ◽  
Continuous Time ◽  
Continuous Time Random Walk

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.

A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS

2015 ◽  
Vol 93 (2) ◽  
pp. 330-339 ◽  
Author(s):  
JONATHAN M. BORWEIN ◽  
CORWIN W. SINNAMON
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Random Walks ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Dimensional Space ◽  
Density Functions ◽  
Piecewise Polynomial ◽  
Odd Dimensions

We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

scholarly journals Mathematical approach to human reaction

2020 ◽  
Author(s):  
Takuya Yabu
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Probability Distribution ◽  
Probability Density ◽  
Density Function ◽  
The Other ◽  
Mathematical Approach ◽  
One Dimensional ◽  
Human Reaction ◽  
Fixed Distribution

I thought about how to get the magnitude from the event and the reaction of the other party. Evaluating the values of events and opponents' reactions using a one-dimensional random walk shows that the probability density function of the values of events and opponents' reactions has a fixed probability distribution. Similarly, I have shown that the functions that determine the magnitude of events and reactions are also represented by a fixed distribution. Therefore, I also showed that when individuals gather to form a group, the functions that determine the magnitude of events and reactions as a group are also represented by a fixed distribution. Also, as an application example of this model, I described how to show my reaction and what to do when the magnitude of the event is large.

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