A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (2) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

A multivariate reward process defined on a semi-Markov process and its first-passage-time distributions

1991 ◽  
Vol 28 (02) ◽  
pp. 360-373 ◽  
Author(s):  
Yasushi Masuda ◽  
Ushio Sumita
Keyword(s):  
Asymptotic Behavior ◽  
Markov Process ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Renewal Equations ◽  
Supplementary Variables ◽  
Semi Markov Process ◽  
Reward Process

A multivariate reward process defined on a semi-Markov process is studied. Transform results for the distributions of the multivariate reward and related processes are derived through the method of supplementary variables and the Markov renewal equations. These transform results enable the asymptotic behavior to be analyzed. A class of first-passage time distributions of the multivariate reward processes is also investigated.

scholarly journals Distributional Properties of Fluid Queues Busy Period and First Passage Times

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1988
Author(s):  
Zbigniew Palmowski
Keyword(s):  
Markov Process ◽  
Busy Period ◽  
First Passage Time ◽  
Passage Time ◽  
Fluid Queue ◽  
First Passage ◽  
Fluid Queues ◽  
Distributional Properties ◽  
Finite State ◽  
Passage Times

In this paper, I analyze the distributional properties of the busy period in an on-off fluid queue and the first passage time in a fluid queue driven by a finite state Markov process. In particular, I show that the first passage time has a IFR distribution and the busy period in the Anick-Mitra-Sondhi model has a DFR distribution.

Exponential trends of first-passage-time densities for a class of diffusion processes with steady-state distribution

1985 ◽  
Vol 22 (3) ◽  
pp. 611-618 ◽  
Author(s):  
A. G. Nobile ◽  
L. M. Ricciardi ◽  
L. Sacerdote
Keyword(s):  
Asymptotic Behavior ◽  
Steady State ◽  
Diffusion Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Steady State Distribution ◽  
State Distribution ◽  
First Passage ◽  
The Mean

The asymptotic behavior of the first-passage-time p.d.f. through a constant boundary is studied when the boundary approaches the endpoints of the diffusion interval. We show that for a class of diffusion processes possessing a steady-state distribution this p.d.f. is approximately exponential, the mean being the average first-passage time to the boundary. The proof is based on suitable recursive expressions for the moments of the first-passage time.

Ageing first-passage times of Markov processes: a matrix approach

1997 ◽  
Vol 34 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Haijun Li ◽  
Moshe Shaked
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
First Passage Time ◽  
Passage Time ◽  
Critical Value ◽  
First Passage Times ◽  
Matrix Approach ◽  
First Passage ◽  
Passage Times

Using a matrix approach we discuss the first-passage time of a Markov process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first-passage time possesses various ageing properties are studied. Some results previously obtained by Li and Shaked (1995) are extended.

scholarly journals -Adic Markov process and the problem of the first return over balls

2021 ◽  
Vol 73 (7) ◽  
pp. 902-912
Author(s):  
O. F. Casas-Sánchez ◽  
J. Galeano-Peñaloza ◽  
J. J. Rodríguez-Vega
Keyword(s):  
Markov Process ◽  
Pseudodifferential Operator ◽  
First Passage Time ◽  
Passage Time ◽  
First Passage ◽  
Time Problem ◽  
First Passage Time Problem

UDC 511.225, 519.217, 511.225.1, 303.532 We consider the pseudodifferential operator defined as where and study the Markov process associated to this operator. We also study the first passage time problem associated to for  

scholarly journals The Renewal Process Generated By Return Times of Semi-Markov Process in Reliability Models

2017 ◽  
Vol 43 (1) ◽  
pp. 365-380
Author(s):  
Franciszek Grabski
Keyword(s):  
Markov Process ◽  
Renewal Process ◽  
First Passage Time ◽  
Return Time ◽  
Passage Time ◽  
Reliability Theory ◽  
Systems Of Equations ◽  
Reliability Models ◽  
Return Times ◽  
Semi Markov Process

Abstract The renewal process generated by the return times of semi-Markov process to a given state is considered in the paper. The return time to a state j and also a first passage time from a given state i to the state j of semi-Markov process are basic concepts that are used to determine this process. The systems of equations for distributions, expectations and secondond moments of these random variables are presented. Theorem concerning the asymptotic distribution of the considered renewal process is presented in this article. Moreover an illustrative example from the reliability theory is presented in the paper.

scholarly journals Limits theorem of first passages times to regenerative processes

2020 ◽  
pp. 57-67
Author(s):  
O. K. Zakusylo ◽  
I. K. Matsak
Keyword(s):  
Asymptotic Behavior ◽  
Queuing Theory ◽  
Statistical Physics ◽  
Extreme Values ◽  
First Passage Time ◽  
Passage Time ◽  
Regenerative Process ◽  
Fixed Number ◽  
Regenerative Processes ◽  
First Passage

The current work continues the author’s investigation in the field of extreme values analysis. The investigation is concerned with the first passage time of a level u for a wide class of regenerative random processes. The common statement of the problem in most of works in the field under consideration dealt with cases when time of observation, t, and u tend to infinity. Alternatively, we investigate the case when t tends to infinity, whereas u is a fixed number. We establish a general limit theorem for the first passage time of a level u by a regenerative process. This topic is closely associated with the asymptotic behavior of extreme values of regenerative processes. In proving the main result, we establish an important lemma concerning the asymptotic behavior of probabilities for a class of random sums, which may be of independent interest. Necessity of the study of such sums occurs in many areas: mathematical reliability theory, queuing theory, some statistical physics problems. In addition, the work provides examples of applications of the obtained general results to some problems, which arise in applied areas: model of counters of type Geiger-Muller, estimation of the reliability of a redundant system with recovery, the problem of the first passage time of a level u by queue length in the queuing system M/M/1.

Sign in / Sign up

Export Citation Format

Share Document