Contact Time in Random Walk and Random Waypoint: Dichotomy in Tail Distribution

Author(s):  
Chen Zhao ◽  
Mihail L. Sichitiu
Author(s):  
Vincent Omollo Nyangaresi ◽  
◽  
Silvance O. Abeka ◽  
Anthony J. Rodrigues

Accurate mobility prediction enables efficient and faster paging services in these networks. This in turn facilitates the attainment of higher bandwidths and execution of activities such as handovers at low latencies. The conventional mobility prediction models operate on unrealistic assumptions that make them unsuitable for cellular network mobile station tracking. For instance, the Feynman-Verlet, first order kinetic model and Random Waypoint assume that mobile phones move with constant velocity while Manhattan, Freeway, city area, street unit, obstacle mobility, and pathway mobility postulate that mobile station movement is restricted along certain paths. In addition, obstacle mobility model speculate that the mobile station signal is completely absorbed by an obstacle while random walk, random waypoint, Markovian random walk, random direction, shortest path model, normal walk, and smooth random assume that a mobile station can move in any direction. Moreover, the greatest challenge of the random direction model is the requirement that a border behavior model be specified for the reaction of mobile stations reaching the simulation area boundary. In this paper, a protocol that addresses the border behavior problem is developed. This protocol is shown to detect when the subscriber has moved out of the current tracking area, which is crucial during handovers.


Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yu Shi ◽  
Qixuan Luo ◽  
Handong Li

In this paper, we propose a new model of security price dynamics in order to explain the stylized facts of the pricing process such as power law distribution, volatility clustering, jumps, and structural changes. We assume that there are two types of agents in the financial market: speculators and fundamental investors. Speculators use past prices to predict future prices and only buy assets whose prices are expected to rise. Fundamental investors attach a certain value to each asset and buy when the asset is undervalued by the market. When the expectations of agents are exogenously driven, that is, entirely shaped by exogenous news, then they can be modeled as following a random walk. We assume that the information related to the two types of agents in the model will arrive randomly with a certain probability distribution and change the viewpoint of the agents according to a certain percentage. Our simulated results show that this model can simulate well the random walk of asset prices and explain the power-law tail distribution of returns, volatility clustering, jumps, and structural changes of asset prices.


Author(s):  
Eyal Neuman ◽  
Xinghua Zheng

AbstractWe consider a branching random walk on $$\mathbb {Z}$$ Z started by n particles at the origin, where each particle disperses according to a mean-zero random walk with bounded support and reproduces with mean number of offspring $$1+\theta /n$$ 1 + θ / n . For $$t\ge 0$$ t ≥ 0 , we study $$M_{nt}$$ M nt , the rightmost position reached by the branching random walk up to generation [nt]. Under certain moment assumptions on the branching law, we prove that $$M_{nt}/\sqrt{n}$$ M nt / n converges weakly to the rightmost support point of the local time of the limiting super-Brownian motion. The convergence result establishes a sharp exponential decay of the tail distribution of $$M_{nt}$$ M nt . We also confirm that when $$\theta >0$$ θ > 0 , the support of the branching random walk grows in a linear speed that is identical to that of the limiting super-Brownian motion which was studied by Pinsky (Ann Probab 23(4):1748–1754, 1995). The rightmost position over all generations, $$M:=\sup _t M_{nt}$$ M : = sup t M nt , is also shown to converge weakly to that of the limiting super-Brownian motion, whose tail is found to decay like a Gumbel distribution when $$\theta <0$$ θ < 0 .


Author(s):  
Joseph Rudnick ◽  
George Gaspari
Keyword(s):  

2014 ◽  
Vol 9 (8) ◽  
pp. 514-518 ◽  
Author(s):  
Wenguo Chen ◽  
Zhaoyu Wang ◽  
Yan Wang ◽  
Zhuoqing Yang ◽  
Guifu Ding ◽  
...  
Keyword(s):  

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