Mixing properties of harris chains and autoregressive processes

1986 ◽  
Vol 23 (4) ◽  
pp. 880-892 ◽  
Author(s):  
Krishna B. Athreya ◽  
Sastry G. Pantula
Keyword(s):  
Sufficient Conditions ◽  
Autoregressive Process ◽  
Strong Mixing ◽  
Stationary Probability ◽  
Autoregressive Processes ◽  
Stationary Probability Distribution ◽  
Mixing Properties ◽  
Recurrent Markov Chain ◽  
General State Space ◽  
Necessary And Sufficient

Let {Yn: n ≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distribution π (·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

Mixing properties of harris chains and autoregressive processes

1986 ◽  
Vol 23 (04) ◽  
pp. 880-892 ◽  
Author(s):  
Krishna B. Athreya ◽  
Sastry G. Pantula
Keyword(s):  
Sufficient Conditions ◽  
Autoregressive Process ◽  
Strong Mixing ◽  
Stationary Probability ◽  
Autoregressive Processes ◽  
Stationary Probability Distribution ◽  
Mixing Properties ◽  
Recurrent Markov Chain ◽  
General State Space ◽  
Necessary And Sufficient

Let {Yn:n≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn} is strong mixing, provided there exists a stationary probability distributionπ(·) for {Yn}. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

Mixing properties of harris chains and autoregressive processes

1986 ◽  
Vol 23 (04) ◽  
pp. 880-892 ◽  
Author(s):  
Krishna B. Athreya ◽  
Sastry G. Pantula
Keyword(s):  
Sufficient Conditions ◽  
Autoregressive Process ◽  
Strong Mixing ◽  
Stationary Probability ◽  
Autoregressive Processes ◽  
Stationary Probability Distribution ◽  
Mixing Properties ◽  
Recurrent Markov Chain ◽  
General State Space ◽  
Necessary And Sufficient

Let {Yn: n ≧ 1} be a Harris-recurrent Markov chain on a general state space. It is shown that {Yn } is strong mixing, provided there exists a stationary probability distribution π (·) for {Yn }. Necessary and sufficient conditions for an autoregressive process to be uniform mixing are given.

PRODUCT-FORM MARKOVIAN QUEUEING SYSTEMS WITH MULTIPLE RESOURCES

2019 ◽  
pp. 1-9 ◽  
Author(s):  
Valeriy Naumov ◽  
Konstantin Samouylov
Keyword(s):  
Queueing Systems ◽  
Sufficient Conditions ◽  
Jump Process ◽  
Product Form ◽  
Temporary Increase ◽  
Stationary Probability Distribution ◽  
Markov Jump ◽  
Multiple Resources ◽  
Resource Requirements ◽  
Necessary And Sufficient

In the paper, we study general Markovian models of loss systems with random resource requirements, in which customers at arrival occupy random quantities of various resources and release them at departure. Customers may request negative quantities of resources, but total amount of resources allocated to customers should be nonnegative and cannot exceed predefined maximum levels. Allocating a negative volume of a resource to a customer leads to a temporary increase in its volume in the system. We derive necessary and sufficient conditions for the product-form of the stationary probability distribution of the Markov jump process describing the system.

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (01) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

Mixing properties of numeration systems coming from weighted substitutions

2009 ◽  
Vol 30 (4) ◽  
pp. 1111-1118
Author(s):  
TETURO KAMAE
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Mixing Properties ◽  
Additive Action ◽  
Strongly Mixing ◽  
Weakly Mixing ◽  
Multiplicative Subgroup ◽  
Numeration Systems ◽  
Tiling Space ◽  
Necessary And Sufficient

AbstractA weighted substitution is a substitution that has weights associated with each occurrence of the substituted symbols. It defines a tiling space that admits the translation and scaling operators; the translation is the additive ℝ-action and the scaling is the multiplicative G-action, where G is a closed multiplicative subgroup of ℝ+. We obtained necessary and sufficient conditions for the additive action to be strongly mixing and for it to be weakly mixing.

Reversibility of Markov chains with applications to storage models

1985 ◽  
Vol 22 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Hideo Ōsawa
Keyword(s):  
Markov Chains ◽  
State Space ◽  
Discrete Time ◽  
Risk Model ◽  
Sufficient Conditions ◽  
Single Server ◽  
General State ◽  
Insurance Risk ◽  
General State Space ◽  
Necessary And Sufficient

This paper studies the reversibility conditions of stationary Markov chains (discrete-time Markov processes) with general state space. In particular, we investigate the Markov chains having atomic points in the state space. Such processes are often seen in storage models, for example waiting time in a queue, insurance risk reserve, dam content and so on. The necessary and sufficient conditions for reversibility of these processes are obtained. Further, we apply these conditions to some storage models and present some interesting results for single-server queues and a finite insurance risk model.

Likelihood ratio gradient estimation for stochastic recursions

1995 ◽  
Vol 27 (04) ◽  
pp. 1019-1053 ◽  
Author(s):  
Peter W. Glynn ◽  
Pierre L'ecuyer
Keyword(s):  
Likelihood Ratio ◽  
Broad Class ◽  
Stationary Probability ◽  
General State ◽  
Change Of Measure ◽  
Gradient Estimation ◽  
Transition Structure ◽  
Ratio Change ◽  
Recurrent Markov Chain ◽  
General State Space

In this paper, we develop mathematical machinery for verifying that a broad class of general state space Markov chains reacts smoothly to certain types of perturbations in the underlying transition structure. Our main result provides conditions under which the stationary probability measure of an ergodic Harris-recurrent Markov chain is differentiable in a certain strong sense. The approach is based on likelihood ratio ‘change-of-measure' arguments, and leads directly to a ‘likelihood ratio gradient estimator' that can be computed numerically.

Limit laws for kth order statistics from strong-mixing processes

1984 ◽  
Vol 21 (04) ◽  
pp. 720-729 ◽  
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Strong Mixing ◽  
Mixing Processes ◽  
Limit Laws ◽  
Independent Case ◽  
Necessary And Sufficient ◽  
Mixing Sequence

We present necessary and sufficient conditions for the weak convergence of the distributions of the kth order statistics from a strictly stationary strong-mixing sequence of random variables to limit laws which are represented in terms of a compound Poisson distribution. The obtained limit laws form a class larger than that occurring in the independent case.

Limit laws for kth order statistics from strong-mixing processes

1984 ◽  
Vol 21 (4) ◽  
pp. 720-729 ◽  
Author(s):  
W. Dziubdziela
Keyword(s):  
Weak Convergence ◽  
Order Statistics ◽  
Poisson Distribution ◽  
Sufficient Conditions ◽  
Strong Mixing ◽  
Mixing Processes ◽  
Limit Laws ◽  
Independent Case ◽  
Necessary And Sufficient ◽  
Mixing Sequence

We present necessary and sufficient conditions for the weak convergence of the distributions of the kth order statistics from a strictly stationary strong-mixing sequence of random variables to limit laws which are represented in terms of a compound Poisson distribution. The obtained limit laws form a class larger than that occurring in the independent case.

scholarly journals Stochastic Lotka-Volterra systems under regime switching with jumps

Filomat ◽  
2014 ◽  
Vol 28 (9) ◽  
pp. 1907-1928 ◽  
Author(s):  
Ruihua Wu ◽  
Xiaoling Zou ◽  
Ke Wang ◽  
Meng Liu
Keyword(s):  
Markov Chain ◽  
Regime Switching ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Stationary Probability ◽  
Stationary Probability Distribution ◽  
Stochastic Permanence ◽  
Color Noise ◽  
Volterra Systems ◽  
The Moment

A stochastic Lotka-Volterra model with Markovian switching driven by jumps is proposed and investigated. In the model, the white noise, color noise and jumping noise are taken into account at the same time. This model is more feasible and applicable. Firstly, sufficient conditions for stochastic permanence and extinction are presented. Then the moment average in time and the asymptotic pathwise properties are estimated. Our results show that these properties have close relations with the jumps and the stationary probability distribution of the Markov chain. Finally, several numerical simulations are provided to illustrate the effectiveness of the results.

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