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.

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.

Addendum to ‘Isotropic correlation functions on d-dimensional balls’

2000 ◽  
Vol 32 (4) ◽  
pp. 960-961
Author(s):  
Tilmann Gneiting
Keyword(s):  
Power Law ◽  
Correlation Functions ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bounded Domains ◽  
Unpublished Work ◽  
Polynomial Models ◽  
Necessary And Sufficient

We discuss necessary and sufficient conditions for power-law and polynomial models to be correlation functions on bounded domains. These results date back to unpublished work by Matheron (1974) and generalize the findings of Gneiting (1999).

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 Sandwich Type Results for m-Convex Real Functions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Teodoro Lara ◽  
Edgar Rosales
Keyword(s):  
Sufficient Conditions ◽  
Jensen’S Inequality ◽  
Geometric Interpretation ◽  
Necessary And Sufficient Conditions ◽  
Affine Function ◽  
Jensen's Inequality ◽  
Real Functions ◽  
Sandwich Type ◽  
Necessary And Sufficient

Abstract We establish necessary and sufficient conditions allowing separation of pair of real functions by an m-convex and by an m-affine function. Some examples and a geometric interpretation of m-convexity of a function is exhibited, as well as a Jensen’s inequality for this kind of function.

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.

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