First passage time of filtered Poisson process with exponential shape function

2005 ◽  
Vol 20 (1) ◽  
pp. 57-65 ◽  
Author(s):  
A. Novikov ◽  
R.E. Melchers ◽  
E. Shinjikashvili ◽  
N. Kordzakhia
Keyword(s):  
Poisson Process ◽  
Shape Function ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage

Time dependent analysis of multivariate marked renewal processes

2001 ◽  
Vol 38 (03) ◽  
pp. 707-721 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Stochastic Models ◽  
First Passage Time ◽  
Compound Poisson Process ◽  
Passage Time ◽  
Time Dependent ◽  
Renewal Processes ◽  
First Passage ◽  
Time Dependent Analysis

The paper examines multivariate delayed marked renewal processes, of which one component is formed by a delayed compound Poisson process observed at epochs of some point process. In addition, the values of these observations (and other components) are watched when crossing their respective thresholds and the value of the original Poisson process at any moment of time, past the first passage time, is the objective of this investigation. The results (which are imperative for classes of semiregenerative processes) are given in closed analytical forms and illustrated on various stochastic models.

Time dependent analysis of multivariate marked renewal processes

2001 ◽  
Vol 38 (3) ◽  
pp. 707-721 ◽  
Author(s):  
Jewgeni H. Dshalalow
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Stochastic Models ◽  
First Passage Time ◽  
Compound Poisson Process ◽  
Passage Time ◽  
Time Dependent ◽  
Renewal Processes ◽  
First Passage ◽  
Time Dependent Analysis

The paper examines multivariate delayed marked renewal processes, of which one component is formed by a delayed compound Poisson process observed at epochs of some point process. In addition, the values of these observations (and other components) are watched when crossing their respective thresholds and the value of the original Poisson process at any moment of time, past the first passage time, is the objective of this investigation. The results (which are imperative for classes of semiregenerative processes) are given in closed analytical forms and illustrated on various stochastic models.

scholarly journals On functionals of a marked Poisson process observed by a renewal process

2001 ◽  
Vol 26 (7) ◽  
pp. 427-436 ◽  
Author(s):  
Jewgeni H. Dshalalow ◽  
Jean-Baptiste Bacot
Keyword(s):  
Laplace Transform ◽  
Poisson Process ◽  
Renewal Process ◽  
Stochastic Models ◽  
First Passage Time ◽  
Passage Time ◽  
Time Dependent ◽  
First Passage ◽  
Time Dependent Solution ◽  
Time Dependent Analysis

We study the functionals of a Poisson marked processΠobserved by a renewal process. A sequence of observations continues untilΠcrosses some fixed level at one of the observation epochs (the first passage time). In various stochastic models applications (such as queueing withN-policy combined with multiple vacations), it is necessary to operate with the value ofΠprior to the first passage time, or prior to the first passage time plus some random time. We obtain a time-dependent solution to this problem in a closed form, in terms of its Laplace transform. Many results are directly applicable to the time-dependent analysis of queues and other stochastic models via semi-regenerative techniques.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

scholarly journals Credit Gap Risk in a First Passage Time Model with Jumps

2009 ◽  
Author(s):  
Natalie Packham ◽  
Lutz Schloegl ◽  
Wolfgang M. Schmidt
Keyword(s):  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Model ◽  
Gap Risk ◽  
Credit Gap
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