scholarly journals Quantitative Bounds for Convergence Rates of Continuous Time Markov Processes

1996 ◽  
Vol 1 (0) ◽  
Author(s):  
Gareth Roberts ◽  
Jeffrey Rosenthal
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Convergence Rates

scholarly journals A continuous-time semi-markov bayesian belief network model for availability measure estimation of fault tolerant systems

2008 ◽  
Vol 28 (2) ◽  
pp. 355-375 ◽  
Author(s):  
Márcio das Chagas Moura ◽  
Enrique López Droguett
Keyword(s):  
Hybrid Model ◽  
Markov Processes ◽  
Continuous Time ◽  
Fault Tolerant ◽  
Numerical Procedure ◽  
Bayesian Belief Networks ◽  
Operational Conditions ◽  
Fault Tolerant Systems ◽  
Semi Markov Processes ◽  
Availability Measure

In this work it is proposed a model for the assessment of availability measure of fault tolerant systems based on the integration of continuous time semi-Markov processes and Bayesian belief networks. This integration results in a hybrid stochastic model that is able to represent the dynamic characteristics of a system as well as to deal with cause-effect relationships among external factors such as environmental and operational conditions. The hybrid model also allows for uncertainty propagation on the system availability. It is also proposed a numerical procedure for the solution of the state probability equations of semi-Markov processes described in terms of transition rates. The numerical procedure is based on the application of Laplace transforms that are inverted by the Gauss quadrature method known as Gauss Legendre. The hybrid model and numerical procedure are illustrated by means of an example of application in the context of fault tolerant systems.

scholarly journals CONVERGENCE RATES OF SUMS OF α-MIXING TRIANGULAR ARRAYS: WITH AN APPLICATION TO NONPARAMETRIC DRIFT FUNCTION ESTIMATION OF CONTINUOUS-TIME PROCESSES

2016 ◽  
Vol 33 (5) ◽  
pp. 1121-1153
Author(s):  
Shin Kanaya
Keyword(s):  
Continuous Time ◽  
Convergence Rates ◽  
Moving Average ◽  
Function Estimation ◽  
Triangular Arrays ◽  
Large Numbers ◽  
Strongly Mixing ◽  
Time Distance ◽  
Continuous Time Processes ◽  
Near Unit Root

The convergence rates of the sums of α-mixing (or strongly mixing) triangular arrays of heterogeneous random variables are derived. We pay particular attention to the case where central limit theorems may fail to hold, due to relatively strong time-series dependence and/or the nonexistence of higher-order moments. Several previous studies have presented various versions of laws of large numbers for sequences/triangular arrays, but their convergence rates were not fully investigated. This study is the first to investigate the convergence rates of the sums of α-mixing triangular arrays whose mixing coefficients are permitted to decay arbitrarily slowly. We consider two kinds of asymptotic assumptions: one is that the time distance between adjacent observations is fixed for any sample size n; and the other, called the infill assumption, is that it shrinks to zero as n tends to infinity. Our convergence theorems indicate that an explicit trade-off exists between the rate of convergence and the degree of dependence. While the results under the infill assumption can be seen as a direct extension of those under the fixed-distance assumption, they are new and particularly useful for deriving sharper convergence rates of discretization biases in estimating continuous-time processes from discretely sampled observations. We also discuss some examples to which our results and techniques are useful and applicable: a moving-average process with long lasting past shocks, a continuous-time diffusion process with weak mean reversion, and a near-unit-root process.

Markovian manpower models in continuous time

1977 ◽  
Vol 14 (02) ◽  
pp. 249-259 ◽  
Author(s):  
Alexander Mehlmann
Keyword(s):  
Markov Processes ◽  
Continuous Time ◽  
Asymptotic Form ◽  
New Approach ◽  
Limiting Behaviour

The problem of determining the asymptotic form of the stock vector n (t) in a continuous time Markovian manpower model is solved for asymptotically exponential recruitment functions {R(t)}. A new approach to the limiting behaviour of some manpower systems with given total sizes {N(t)} is then given by means of time-inhomogeneous Markov processes.

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