Tests for semiparametric model based on non-homogeneous Markov process

1996 ◽  
Vol 27 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Leszek Marzec ◽  
Pawel Marzec
Keyword(s):  
Markov Process ◽  
Semiparametric Model ◽  
Homogeneous Markov Process ◽  
Model Based

Extension of Wald's first lemma to Markov processes

1999 ◽  
Vol 36 (01) ◽  
pp. 48-59 ◽  
Author(s):  
George V. Moustakides
Keyword(s):  
Integral Equation ◽  
Markov Process ◽  
Markov Processes ◽  
Correction Term ◽  
Stopping Time ◽  
Poisson Integral ◽  
Homogeneous Markov Process ◽  
Partial Sum ◽  
Poisson Integral Equation ◽  
Scalar Nonlinearity

Let ξ0,ξ1,ξ2,… be a homogeneous Markov process and let S n denote the partial sum S n = θ(ξ1) + … + θ(ξ n ), where θ(ξ) is a scalar nonlinearity. If N is a stopping time with 𝔼N < ∞ and the Markov process satisfies certain ergodicity properties, we then show that 𝔼S N = [lim n→∞𝔼θ(ξ n )]𝔼N + 𝔼ω(ξ0) − 𝔼ω(ξ N ). The function ω(ξ) is a well defined scalar nonlinearity directly related to θ(ξ) through a Poisson integral equation, with the characteristic that ω(ξ) becomes zero in the i.i.d. case. Consequently our result constitutes an extension to Wald's first lemma for the case of Markov processes. We also show that, when 𝔼N → ∞, the correction term is negligible as compared to 𝔼N in the sense that 𝔼ω(ξ0) − 𝔼ω(ξ N ) = o(𝔼N).

Proportional intensities and strong ergodicity for Markov processes

1983 ◽  
Vol 20 (01) ◽  
pp. 185-190 ◽  
Author(s):  
Mark Scott ◽  
Dean L. Isaacson
Keyword(s):  
Markov Process ◽  
Markov Processes ◽  
Discrete Time ◽  
Continuous Time ◽  
Homogeneous Markov Process ◽  
Strong Ergodicity ◽  
Transition Functions ◽  
The Matrix ◽  
Intensity Functions ◽  
Time Point

By assuming the proportionality of the intensity functions at each time point for a continuous-time non-homogeneous Markov process, strong ergodicity for the process is determined through strong ergodicity of a related discrete-time Markov process. For processes having proportional intensities, strong ergodicity implies having the limiting matrix L satisfy L · P(s, t) = L, where P(s, t) is the matrix of transition functions.

scholarly journals A novel wideband dynamic directional indoor channel model based on a Markov process

2005 ◽  
Vol 4 (4) ◽  
pp. 1539-1552 ◽  
Author(s):  
Chia-Chin Chong ◽  
Chor-Min Tan ◽  
D.I. Laurenson ◽  
S. McLaughlin ◽  
M.A. Beach ◽  
...  
Keyword(s):  
Markov Process ◽  
Channel Model ◽  
Model Based

Optimality of the one step look-ahead stopping times

1977 ◽  
Vol 14 (1) ◽  
pp. 162-169 ◽  
Author(s):  
M. Abdel-Hameed
Keyword(s):  
Markov Process ◽  
Discrete Time ◽  
Measurable Function ◽  
Infinitesimal Generator ◽  
Stopping Time ◽  
Stopping Times ◽  
Homogeneous Markov Process ◽  
Look Ahead ◽  
One Step ◽  
The One

The optimality of the one step look-ahead stopping rule is shown to hold under conditions different from those discussed by Chow, Robbins and Seigmund [5]. These results are corollaries of the following theorem: Let {Xn, n = 0, 1, …}; X0 = x be a discrete-time homogeneous Markov process with state space (E, ℬ). For any ℬ-measurable function g and α in (0, 1], define Aαg(x) = αExg(X1) – g(x) to be the infinitesimal generator of g. If τ is any stopping time satisfying the conditions: Ex[αNg(XN)I(τ > N)]→0 as as N → ∞, then Applications of the results are considered.

scholarly journals Closed-form solution for the distribution of the total time spent in a subset of states of a homogeneous Markov process during a finite observation period

1990 ◽  
Vol 27 (3) ◽  
pp. 713-719 ◽  
Author(s):  
Bruno Sericola
Keyword(s):  
Markov Process ◽  
Closed Form ◽  
Fault Tolerant ◽  
Computer Systems ◽  
Closed Form Solution ◽  
Form Solution ◽  
Homogeneous Markov Process ◽  
Markovian Processes ◽  
Finite Observation ◽  
Observation Period

Markov process are widely used to model computer systems. De Souza e Silva and Gail [3] calculated numerically the distribution of the cumulative operational time of repairable computer systems modelled by Markovian processes, that is, the distribution of the total time during which the system was in operation over a finite observation period. An extension of their approach is presented here. A closed-form solution is obtained for the distribution of the total time spent in a subset of states of a homogeneous Markov process during a finite observation period, which is theoretically and numerically interesting. We also give an application of this result to a fault-tolerant system.

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