First exit times and diffusion approximations for storage models with Poisson inputs, Poisson outputs and deterministic release rule

OPSEARCH ◽  
2013 ◽  
Vol 50 (4) ◽  
pp. 566-581 ◽  
Author(s):  
P. R. Vittal ◽  
M. Venkateswaran ◽  
P. R. S. Reddy
Keyword(s):  
Diffusion Approximations ◽  
Exit Times ◽  
First Exit Times ◽  
And Diffusion

Well-timed diffusion approximations

1981 ◽  
Vol 13 (2) ◽  
pp. 352-368 ◽  
Author(s):  
John B. Walsh
Keyword(s):  
Markov Process ◽  
Diffusion Process ◽  
Diffusion Approximation ◽  
Asymptotic Approximation ◽  
Stopping Times ◽  
Diffusion Approximations ◽  
Exit Times ◽  
Special Cases ◽  
Exit Probabilities ◽  
First Exit Times

Let X be a Markov process on the line. Under certain conditions it is possible to find a diffusion process which is an approximation to X in the following sense:(1) X can be embedded in that is there are stopping times (Tt) such that {Xt, t ≥ 0} and have the same distribution;(2) for each t, E{Tt} = t.We call the well-timed diffusion approximation to X, and suggest that it is useful for approximating quantities like the first-exit probabilities and expected first-exit times of X.We determine the well-timed approximation in several special cases and give an asymptotic approximation for use in cases in which cannot be exactly determined.

Well-timed diffusion approximations

1981 ◽  
Vol 13 (02) ◽  
pp. 352-368 ◽  
Author(s):  
John B. Walsh
Keyword(s):  
Markov Process ◽  
Diffusion Process ◽  
Diffusion Approximation ◽  
Asymptotic Approximation ◽  
Stopping Times ◽  
Diffusion Approximations ◽  
Exit Times ◽  
Special Cases ◽  
Exit Probabilities ◽  
First Exit Times

LetXbe a Markov process on the line. Under certain conditions it is possible to find a diffusion processwhich is an approximation toXin the following sense:(1)Xcan be embedded inthat is there are stopping times (Tt) such that {Xt,t≥ 0} andhave the same distribution;(2) for eacht,E{Tt} =t.We callthe well-timed diffusion approximation toX, and suggest that it is useful for approximating quantities like the first-exit probabilities and expected first-exit times ofX.We determine the well-timed approximation in several special cases and give an asymptotic approximation for use in cases in whichcannot be exactly determined.

scholarly journals A review of the deterministic and diffusion approximations for stochastic chemical reaction networks

2018 ◽  
Vol 123 (2) ◽  
pp. 289-312 ◽  
Author(s):  
Pavel Mozgunov ◽  
Marco Beccuti ◽  
Andras Horvath ◽  
Thomas Jaki ◽  
Roberta Sirovich ◽  
...  
Keyword(s):  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Diffusion Approximations ◽  
And Diffusion

scholarly journals Simulation of stochastic diffusion via first exit times

2015 ◽  
Vol 300 ◽  
pp. 862-886 ◽  
Author(s):  
Per Lötstedt ◽  
Lina Meinecke
Keyword(s):  
Exit Times ◽  
Stochastic Diffusion ◽  
First Exit Times
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