Necessary and sufficient conditions on the parameters of 1-D Gaussian Markov processes

1992 ◽  
Vol 40 (5) ◽  
pp. 1266-1271 ◽  
Author(s):  
S. Lakshmanan ◽  
K. Derin
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient

Insensitivity and reversed Markov processes

1983 ◽  
Vol 15 (4) ◽  
pp. 752-768 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

Insensitivity and reversed Markov processes

1983 ◽  
Vol 15 (04) ◽  
pp. 752-768 ◽  
Author(s):  
W. Henderson
Keyword(s):  
Markov Processes ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
The Relationship

This paper is concerned with the relationship between insensitivity in a certain class of Markov processes and properties of that process when time is reversed. Necessary and sufficient conditions for insensitivity are established and linked to already proved results. A number of examples of insensitive systems are given.

scholarly journals Weak convergence of first-rare-event times for semi-Markov processes

2020 ◽  
Author(s):  
AISDL
Keyword(s):  
Weak Convergence ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Rare Event ◽  
Necessary And Sufficient Conditions ◽  
Finite Set ◽  
In Series ◽  
Event Times ◽  
Semi Markov Processes ◽  
Necessary And Sufficient

Necessary and sufficient conditions for weak convergence of first-rareevent times for semi-Markov processes with finite set of states in series of schemes are obtained.

COPULA-BASED CHARACTERIZATIONS FOR HIGHER ORDER MARKOV PROCESSES

2009 ◽  
Vol 25 (3) ◽  
pp. 819-846 ◽  
Author(s):  
Rustam Ibragimov
Keyword(s):  
Time Series ◽  
Markov Processes ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Conditional Symmetry ◽  
Finite Dimensional ◽  
Necessary And Sufficient ◽  
Dependence Properties

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibitm-dependence,r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness withm-dependence orr-independence in time series.

ON THE MONOTONICITY OF FLUCTUATION SPECTRA FOR THREE-STATE MARKOV PROCESSES

2007 ◽  
Vol 07 (03) ◽  
pp. L181-L192 ◽  
Author(s):  
YONG CHEN
Keyword(s):  
Time Scales ◽  
Markov Processes ◽  
Correlation Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fluctuation Spectrum ◽  
Real Functions ◽  
Explicit Formulae ◽  
Necessary And Sufficient

Explicit formulae for correlation functions and fluctuation spectra of the irreducible three-state Markov processes are presented. The necessary and sufficient conditions of existing nonmonotonic fluctuation spectra on [0, +∞) with respect to real functions are given, which reveals that the nonequilibrium flux must be strong enough to produce a peak in the fluctuation spectrum and the monotonicity of fluctuation spectra is related to the time scales of Markov processes.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

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