Convergence theorems for queueing and waiting-time processes with continuous time

1977 ◽  
Vol 28 (5) ◽  
pp. 475-482
Author(s):  
N. P. Leont'eva
Keyword(s):  
Waiting Time ◽  
Continuous Time ◽  
Convergence Theorems

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

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.

The relative efficiency of direct and maximum likelihood estimates of mean waiting time in the simple queue, M/M/1

1972 ◽  
Vol 9 (2) ◽  
pp. 396-403 ◽  
Author(s):  
John H. Jenkins
Keyword(s):  
Maximum Likelihood ◽  
Waiting Time ◽  
Continuous Time ◽  
Relative Efficiency ◽  
Asymptotic Variance ◽  
Complete Information ◽  
Maximum Likelihood Estimates ◽  
Time Study ◽  
Direct Estimate ◽  
Mean Waiting Time

A problem of estimating waiting time in the statistical analysis of queues is investigated. The continuous time study of the M/M/1 queue made by Bailey is adapted to obtain the asymptotic variance of a direct estimate of waiting time as obtained under conditions of incomplete information. This is then compared with the asymptotic variance of the maximum likelihood estimate as obtained under conditions of complete information and based on the results of Clarke.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

2018 ◽  
Vol 20 (32) ◽  
pp. 20827-20848 ◽  
Author(s):  
Ru Hou ◽  
Andrey G. Cherstvy ◽  
Ralf Metzler ◽  
Takuma Akimoto
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Power Law ◽  
Waiting Time ◽  
Continuous Time ◽  
Zero Drift ◽  
Renewal Processes ◽  
Waiting Time Distributions ◽  
Continuous Time Random Walks ◽  
Ergodicity Breaking

We examine renewal processes with power-law waiting time distributions and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics.

Limit theorem for continuous-time random walks with two time scales

2004 ◽  
Vol 41 (2) ◽  
pp. 455-466 ◽  
Author(s):  
Peter Becker-Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Time Scales ◽  
Waiting Time ◽  
Continuous Time ◽  
Fractional Partial Differential Equations ◽  
Finite Dimensional ◽  
Mean Waiting Time ◽  
Continuous Time Random Walks ◽  
Random Jumps ◽  
The Mean

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

Limit theorem for continuous-time random walks with two time scales

2004 ◽  
Vol 41 (02) ◽  
pp. 455-466 ◽  
Author(s):  
Peter Becker-Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Time Scales ◽  
Waiting Time ◽  
Continuous Time ◽  
Fractional Partial Differential Equations ◽  
Finite Dimensional ◽  
Mean Waiting Time ◽  
Continuous Time Random Walks ◽  
Random Jumps ◽  
The Mean

Continuous-time random walks incorporate a random waiting time between random jumps. They are used in physics to model particle motion. A physically realistic rescaling uses two different time scales for the mean waiting time and the deviation from the mean. This paper derives the scaling limits for such processes. These limit processes are governed by fractional partial differential equations that may be useful in physics. A transfer theorem for weak convergence of finite-dimensional distributions of stochastic processes is also obtained.

On some waiting time problems

2000 ◽  
Vol 37 (03) ◽  
pp. 756-764 ◽  
Author(s):  
Valeri T. Stefanov
Keyword(s):  
Survival Analysis ◽  
Finite Number ◽  
Markov Processes ◽  
Waiting Time ◽  
Generating Functions ◽  
Continuous Time ◽  
Waiting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Semi Markov Processes

A unifying technology is introduced for finding explicit closed form expressions for joint moment generating functions of various random quantities associated with some waiting time problems. Sooner and later waiting times are covered for general discrete- and continuous-time models. The models are either Markov chains or semi-Markov processes with a finite number of states. Waiting times associated with generalized phase-type distributions, that are of interest in survival analysis and other areas, are also covered.

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