Coupling Methods for Markov Chains and the Renewal Theorem for Lattice Distributions

2021 ◽  
pp. 99-112
Author(s):  
Rabi Bhattacharya ◽  
Edward C. Waymire
Keyword(s):  
Markov Chains ◽  
Renewal Theorem ◽  
Coupling Methods

Asymptotic and monotonicity properties of some repairable systems

1998 ◽  
Vol 30 (4) ◽  
pp. 1089-1110 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Repairable Systems ◽  
Lifetime Distributions ◽  
Failure Times ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Monotonicity Properties ◽  
Heavy Tailed

The paper studies a model of repairable systems which is flexible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes-type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak total variation and moment convergences are obtained and illustrated by examples with IFR, DFR, heavy-tailed and light-tailed lifetime distributions. Some convergences obtained are monotone and/or at a geometric rate.

SHIFT AND SCALE COUPLING METHODS FOR PERFECT SIMULATION

2003 ◽  
Vol 17 (3) ◽  
pp. 277-303 ◽  
Author(s):  
J.N. Corcoran ◽  
U. Schneider
Keyword(s):  
Markov Chains ◽  
Sampling Procedure ◽  
Attractive Alternative ◽  
Density Functions ◽  
Perfect Simulation ◽  
Perfect Sampling ◽  
Slice Sampling ◽  
Sample Paths ◽  
Coupling Methods ◽  
Sampling Algorithms

We describe and develop a variation on a layered multishift coupler due to Wilson that uses a slice sampling procedure to allow one to obtain potentially common draws from two different distributions. Our main application is coupling sample paths of Markov chains for use in perfect sampling algorithms. The coupler is based on slicing density functions and we describe a “folding” mechanism as an attractive alternative to the accept/reject step commonly used in slice sampling algorithms. Applications of the coupler are given to storage models and to auto-gamma distribution sampling.

Asymptotic and monotonicity properties of some repairable systems

1998 ◽  
Vol 30 (04) ◽  
pp. 1089-1110 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Repairable Systems ◽  
Lifetime Distributions ◽  
Failure Times ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Monotonicity Properties ◽  
Heavy Tailed

The paper studies a model of repairable systems which is flexible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes-type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak total variation and moment convergences are obtained and illustrated by examples with IFR, DFR, heavy-tailed and light-tailed lifetime distributions. Some convergences obtained are monotone and/or at a geometric rate.

scholarly journals Coupling methods for random topological Markov chains

2015 ◽  
Vol 37 (3) ◽  
pp. 971-994 ◽  
Author(s):  
MANUEL STADLBAUER
Keyword(s):  
Markov Chains ◽  
Spectral Gap ◽  
Shift Spaces ◽  
Transfer Operators ◽  
Coupling Methods ◽  
Coupling Techniques

We apply coupling techniques in order to prove that the transfer operators associated with random topological Markov chains and non-stationary shift spaces with the big images and preimages property have a spectral gap.

Markov models—Markov chains

2019 ◽  
Vol 16 (8) ◽  
pp. 663-664 ◽  
Author(s):  
Jasleen K. Grewal ◽  
Martin Krzywinski ◽  
Naomi Altman
Keyword(s):  
Markov Chains ◽  
Markov Models

Synchronization of Chaotic Quantum Dot Light Emitting Diodes under Optical Feedback Effect

2020 ◽  
pp. 144-148
Keyword(s):  
Quantum Dot ◽  
Delay Time ◽  
Chaos Synchronization ◽  
Optical Feedback ◽  
Light Emitting Diode ◽  
Feedback Effect ◽  
Complete Synchronization ◽  
Light Emitting ◽  
Coupling Methods ◽  
Coupling Parameters

Chaos synchronization of delayed quantum dot light emitting diode has been studied theortetically which are coupled via the unidirectional and bidirectional. at synchronization of chaotic, The dynamics is identical with delayed optical feedback for those coupling methods. Depending on the coupling parameters and delay time the system exhibits complete synchronization, . Under proper conditions, the receiver quantum dot light emitting diode can be satisfactorily synchronized with the transmitter quantum dot light emitting diode due to the optical feedback effect.

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