Journal articles: 'Harris chains'

1

Corcoran, J. N., and R. L. Tweedie. "Perfect sampling of ergodic Harris chains." Annals of Applied Probability 11, no. 2 (May 2001): 438–51. http://dx.doi.org/10.1214/aoap/1015345299.

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2

Sigman, Karl. "Queues as Harris recurrent Markov chains." Stochastic Processes and their Applications 26 (1987): 225. http://dx.doi.org/10.1016/0304-4149(87)90154-2.

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3

Sigman, Karl. "Queues as Harris recurrent Markov chains." Queueing Systems 3, no. 2 (June 1988): 179–98. http://dx.doi.org/10.1007/bf01189048.

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4

Malinovskii, V. K. "Limit Theorems for Harris Markov Chains, I." Theory of Probability & Its Applications 31, no. 2 (June 1987): 269–85. http://dx.doi.org/10.1137/1131033.

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5

Malinovskii, V. K. "Limit Theorems for Harris Markov Chains, II." Theory of Probability & Its Applications 34, no. 2 (January 1990): 252–65. http://dx.doi.org/10.1137/1134021.

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6

Fralix, Brian H. "Foster-type criteria for Markov chains on general spaces." Journal of Applied Probability 43, no. 04 (December 2006): 1194–200. http://dx.doi.org/10.1017/s0021900200002540.

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This paper establishes new Foster-type criteria for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent, or geometrically ergodic. The criteria are based on drift conditions involving stopping times rather than deterministic steps. Meyn and Tweedie (1994) developed similar criteria involving random-sized steps, independent of the Markov chain under study. They also posed an open problem of finding criteria involving stopping times. Our results essentially solve that problem. We also show that the assumption of ψ-irreducibility is not needed when stating our drift conditions for positive Harris recurrence or geometric ergodicity.

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7

Fralix, Brian H. "Foster-type criteria for Markov chains on general spaces." Journal of Applied Probability 43, no. 4 (December 2006): 1194–200. http://dx.doi.org/10.1239/jap/1165505219.

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This paper establishes new Foster-type criteria for a Markov chain on a general state space to be Harris recurrent, positive Harris recurrent, or geometrically ergodic. The criteria are based on drift conditions involving stopping times rather than deterministic steps. Meyn and Tweedie (1994) developed similar criteria involving random-sized steps, independent of the Markov chain under study. They also posed an open problem of finding criteria involving stopping times. Our results essentially solve that problem. We also show that the assumption of ψ-irreducibility is not needed when stating our drift conditions for positive Harris recurrence or geometric ergodicity.

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8

Athreya, Krishna B., and Sastry G. Pantula. "Mixing properties of harris chains and autoregressive processes." Journal of Applied Probability 23, no. 4 (December 1986): 880–92. http://dx.doi.org/10.2307/3214462.

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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.

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9

Athreya, Krishna B., and Sastry G. Pantula. "Mixing properties of harris chains and autoregressive processes." Journal of Applied Probability 23, no. 04 (December 1986): 880–92. http://dx.doi.org/10.1017/s0021900200116067.

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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.

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10

Athreya, Krishna B., and Sastry G. Pantula. "Mixing properties of harris chains and autoregressive processes." Journal of Applied Probability 23, no. 04 (December 1986): 880–92. http://dx.doi.org/10.1017/s0021900200118674.

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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.

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11

Malinovskii, V. K. "Addendum: Limit Theorems for Harris Markov Chains. I." Theory of Probability & Its Applications 36, no. 2 (January 1992): 426. http://dx.doi.org/10.1137/1136053.

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12

Levental, Shlomo. "Uniform limit theorems for Harris recurrent Markov chains." Probability Theory and Related Fields 80, no. 1 (1988): 101–18. http://dx.doi.org/10.1007/bf00348754.

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13

Glynn, Peter W., and Chang-Han Rhee. "Exact estimation for Markov chain equilibrium expectations." Journal of Applied Probability 51, A (December 2014): 377–89. http://dx.doi.org/10.1017/s0021900200021392.

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We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

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14

Glynn, Peter W., and Chang-Han Rhee. "Exact estimation for Markov chain equilibrium expectations." Journal of Applied Probability 51, A (December 2014): 377–89. http://dx.doi.org/10.1239/jap/1417528487.

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We introduce a new class of Monte Carlo methods, which we call exact estimation algorithms. Such algorithms provide unbiased estimators for equilibrium expectations associated with real-valued functionals defined on a Markov chain. We provide easily implemented algorithms for the class of positive Harris recurrent Markov chains, and for chains that are contracting on average. We further argue that exact estimation in the Markov chain setting provides a significant theoretical relaxation relative to exact simulation methods.

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15

Asmussen, Søren, and Hermann Thorisson. "A Markov chain approach to periodic queues." Journal of Applied Probability 24, no. 1 (March 1987): 215–25. http://dx.doi.org/10.2307/3214072.

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We consider GI/G/1 queues in an environment which is periodic in the sense that the service time of the nth customer and the next interarrival time depend on the phase θ n at the arrival instant. Assuming Harris ergodicity of {θ n} and a suitable condition on the traffic intensity, various Markov chains related to the queue are then again Harris ergodic and provide limit results for the standard customer- and time-dependent processes such as waiting times and queue lengths. As part of the analysis, a result of Nummelin (1979) concerning Lindley processes on a Markov chain is reconsidered.

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16

Asmussen, Søren, and Hermann Thorisson. "A Markov chain approach to periodic queues." Journal of Applied Probability 24, no. 01 (March 1987): 215–25. http://dx.doi.org/10.1017/s0021900200030746.

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We consider GI/G/1 queues in an environment which is periodic in the sense that the service time of the nth customer and the next interarrival time depend on the phase θ n at the arrival instant. Assuming Harris ergodicity of {θ n } and a suitable condition on the traffic intensity, various Markov chains related to the queue are then again Harris ergodic and provide limit results for the standard customer- and time-dependent processes such as waiting times and queue lengths. As part of the analysis, a result of Nummelin (1979) concerning Lindley processes on a Markov chain is reconsidered.

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17

Sancetta, Alessio. "Nearest neighbor conditional estimation for Harris recurrent Markov chains." Journal of Multivariate Analysis 100, no. 10 (November 2009): 2224–36. http://dx.doi.org/10.1016/j.jmva.2009.06.013.

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18

Li, Degui, Dag Tjøstheim, and Jiti Gao. "Estimation in nonlinear regression with Harris recurrent Markov chains." Annals of Statistics 44, no. 5 (October 2016): 1957–87. http://dx.doi.org/10.1214/15-aos1379.

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19

Hernández-Lerma, Onésimo, and Jean B. Lasserre. "Further criteria for positive Harris recurrence of Markov chains." Proceedings of the American Mathematical Society 129, no. 5 (October 24, 2000): 1521–24. http://dx.doi.org/10.1090/s0002-9939-00-05672-0.

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20

Anichkin, S. A. "Estimating the approximation accuracy of Harris-recurrent Markov chains." Journal of Soviet Mathematics 35, no. 2 (October 1986): 2301–6. http://dx.doi.org/10.1007/bf01105646.

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21

Glynn, Peter W. "On exponential limit laws for hitting times of rare sets for Harris chains and processes." Journal of Applied Probability 48, A (August 2011): 319–26. http://dx.doi.org/10.1017/s0021900200099319.

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This paper provides a simple proof for the fact that the hitting time to an infrequently visited subset for a one-dependent regenerative process converges weakly to an exponential distribution. Special cases are positive recurrent Harris chains and Harris processes. The paper further extends this class of limit theorems to ‘rewards’ that are cumulated to the hitting time of such a rare set.

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22

Glynn, Peter W. "On exponential limit laws for hitting times of rare sets for Harris chains and processes." Journal of Applied Probability 48, A (August 2011): 319–26. http://dx.doi.org/10.1239/jap/1318940474.

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This paper provides a simple proof for the fact that the hitting time to an infrequently visited subset for a one-dependent regenerative process converges weakly to an exponential distribution. Special cases are positive recurrent Harris chains and Harris processes. The paper further extends this class of limit theorems to ‘rewards’ that are cumulated to the hitting time of such a rare set.

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23

DERRIENNIC, YVES, and MICHAEL LIN. "VARIANCE BOUNDING MARKOV CHAINS, L2-UNIFORM MEAN ERGODICITY AND THE CLT." Stochastics and Dynamics 11, no. 01 (March 2011): 81–94. http://dx.doi.org/10.1142/s0219493711003176.

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We prove that variance bounding Markov chains, as defined by Roberts and Rosenthal [31], are uniformly mean ergodic in L2 of the invariant probability. For such chains, without any additional mixing, reversibility, or Harris recurrence assumptions, the central limit theorem and the invariance principle hold for every centered additive functional with finite variance. We also show that L2-geometric ergodicity is equivalent to L2-uniform geometric ergodicity. We then specialize the results to random walks on compact Abelian groups, and construct a probability on the unit circle such that the random walk it generates is L2-uniformly geometrically ergodic, but is not Harris recurrent.

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24

Chen, Xia. "Some dichotomy results for functionals of Harris recurrent Markov chains." Stochastic Processes and their Applications 83, no. 1 (September 1999): 211–36. http://dx.doi.org/10.1016/s0304-4149(99)00038-1.

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25

Hu, Feng-Rung. "ON CONVERGENT RATES OF ERGODIC HARRIS CHAINS INDUCED FROM DIFFUSIONS." Taiwanese Journal of Mathematics 10, no. 3 (March 2006): 651–68. http://dx.doi.org/10.11650/twjm/1500403853.

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26

Ciołek, Gabriela. "Bootstrap uniform central limit theorems for Harris recurrent Markov chains." Electronic Journal of Statistics 10, no. 2 (2016): 2157–78. http://dx.doi.org/10.1214/16-ejs1167.

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27

Chen, X. "The functional moderate deviations for Harris recurrent Markov chains and applications." Annales de l'Institut Henri Poincare (B) Probability and Statistics 40, no. 1 (February 2004): 89–124. http://dx.doi.org/10.1016/s0246-0203(03)00061-x.

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28

CHEN, X. "The functional moderate deviations for Harris recurrent Markov chains and applications." Annales de l?Institut Henri Poincare (B) Probability and Statistics 40, no. 1 (February 2004): 89–124. http://dx.doi.org/10.1016/j.anihpb.2003.07.002.

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29

Roberts, Gareth O., and Jeffrey S. Rosenthal. "Harris recurrence of Metropolis-within-Gibbs and trans-dimensional Markov chains." Annals of Applied Probability 16, no. 4 (November 2006): 2123–39. http://dx.doi.org/10.1214/105051606000000510.

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30

Hooghiemstra, G., and M. Keane. "Calculation of the equilibrium distribution for a solar energy storage model." Journal of Applied Probability 22, no. 4 (December 1985): 852–64. http://dx.doi.org/10.2307/3213953.

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The study of simple solar energy storage models leads to the question of analyzing the equilibrium distribution of Markov chains (Harris chains), for which the state at epoch (n + 1) (i.e. the temperature of the storage tank) depends on the state at epoch n and on a controlled input, acceptance of which entails a further decrease of the temperature level. Here we study the model where the input is exponentially distributed. For all values of the parameters involved an explicit expression for the equilibrium distribution of the Markov chain is derived, and from this we calculate, as one of the possible applications, the exact values of the mean of this equilibrium distribution.

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31

Hooghiemstra, G., and M. Keane. "Calculation of the equilibrium distribution for a solar energy storage model." Journal of Applied Probability 22, no. 04 (December 1985): 852–64. http://dx.doi.org/10.1017/s0021900200108095.

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The study of simple solar energy storage models leads to the question of analyzing the equilibrium distribution of Markov chains (Harris chains), for which the state at epoch (n + 1) (i.e. the temperature of the storage tank) depends on the state at epoch n and on a controlled input, acceptance of which entails a further decrease of the temperature level. Here we study the model where the input is exponentially distributed. For all values of the parameters involved an explicit expression for the equilibrium distribution of the Markov chain is derived, and from this we calculate, as one of the possible applications, the exact values of the mean of this equilibrium distribution.

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32

Glynn, Peter W., and Pierre L'ecuyer. "Likelihood ratio gradient estimation for stochastic recursions." Advances in Applied Probability 27, no. 04 (December 1995): 1019–53. http://dx.doi.org/10.1017/s0001867800047789.

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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.

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33

Glynn, Peter W., and Pierre L'ecuyer. "Likelihood ratio gradient estimation for stochastic recursions." Advances in Applied Probability 27, no. 4 (December 1995): 1019–53. http://dx.doi.org/10.2307/1427933.

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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.

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34

Feigin, Paul D., and Richard L. Tweedie. "Linear functionals and Markov chains associated with Dirichlet processes." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 3 (May 1989): 579–85. http://dx.doi.org/10.1017/s0305004100077951.

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AbstractBy investigating a Markov chain whose limiting distribution corresponds to that of the Dirichlet process we are able directly to ascertain conditions for the existence of linear functionals of that process. Together with earlier analyses we are able to characterize those functionals which are a.s. finite in terms of the parameter measure of the process. We also show that the appropriate Markov chain in the space of measures is only weakly convergent and not Harris ergodic.

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35

Meyn, Sean P., and R. L. Tweedie. "Stability of Markovian processes I: criteria for discrete-time Chains." Advances in Applied Probability 24, no. 03 (September 1992): 542–74. http://dx.doi.org/10.1017/s000186780002440x.

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In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the other. We show that these concepts of stability are largely equivalent for a major class of chains (chains with continuous components), or if the state space has a sufficiently rich class of appropriate sets (‘petite sets'). We use a discrete formulation of Dynkin's formula to establish unified criteria for these stability concepts, through bounding of moments of first entrance times to petite sets. This gives a generalization of Lyapunov–Foster criteria for the various stability conditions to hold. Under these criteria, ergodic theorems are shown to be valid even in the non-irreducible case. These results allow a more general test function approach for determining rates of convergence of the underlying distributions of a Markov chain, and provide strong mixing results and new versions of the central limit theorem and the law of the iterated logarithm.

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36

Meyn, Sean P., and R. L. Tweedie. "Stability of Markovian processes I: criteria for discrete-time Chains." Advances in Applied Probability 24, no. 3 (September 1992): 542–74. http://dx.doi.org/10.2307/1427479.

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In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the other. We show that these concepts of stability are largely equivalent for a major class of chains (chains with continuous components), or if the state space has a sufficiently rich class of appropriate sets (‘petite sets').We use a discrete formulation of Dynkin's formula to establish unified criteria for these stability concepts, through bounding of moments of first entrance times to petite sets. This gives a generalization of Lyapunov–Foster criteria for the various stability conditions to hold. Under these criteria, ergodic theorems are shown to be valid even in the non-irreducible case. These results allow a more general test function approach for determining rates of convergence of the underlying distributions of a Markov chain, and provide strong mixing results and new versions of the central limit theorem and the law of the iterated logarithm.

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37

Samur, Jorge D. "A regularity condition and a limit theorem for Harris ergodic Markov chains." Stochastic Processes and their Applications 111, no. 2 (June 2004): 207–35. http://dx.doi.org/10.1016/j.spa.2004.02.005.

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38

Liebscher, E., and H. Schäbe. "A generalization of the Kaplan-Meier estimator to Harris-recurrent Markov chains." Statistical Papers 38, no. 1 (March 1997): 63–75. http://dx.doi.org/10.1007/bf02925215.

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39

GORDIN, MIKHAIL, and HAJO HOLZMANN. "THE CENTRAL LIMIT THEOREM FOR STATIONARY MARKOV CHAINS UNDER INVARIANT SPLITTINGS." Stochastics and Dynamics 04, no. 01 (March 2004): 15–30. http://dx.doi.org/10.1142/s0219493704000985.

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The central limit theorem (CLT) for stationary ergodic Markov chains is investigated. We give a short survey of related results on the CLT for general (not necessarily Harris recurrent) chains and formulate a new sufficient condition for its validity. Furthermore, Markov operators are considered which admit invariant orthogonal splittings of the space of square-integrable functions. We show how conditions for the CLT can be improved if this additional structure is taken into account. Finally we give examples of this situation, namely endomorphisms of compact Abelian groups and random walks on compact homogeneous spaces.

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40

Borovkov, A. A. "Conditions for ergodicity of Markov chains which are not associated with Harris irreducibility." Siberian Mathematical Journal 32, no. 4 (1992): 543–54. http://dx.doi.org/10.1007/bf00972973.

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41

Bandi, Federico M., and Valentina Corradi. "NONPARAMETRIC NONSTATIONARITY TESTS." Econometric Theory 30, no. 1 (August 20, 2013): 127–49. http://dx.doi.org/10.1017/s0266466613000145.

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We propose additive functional-based nonstationarity tests that exploit the different divergence rates of the occupation times of a (possibly nonlinear) process under the null of nonstationarity (stationarity) versus the alternative of stationarity (nonstationarity). We consider both discrete-time series and continuous-time processes. The discrete-time case covers Harris recurrent Markov chains and integrated processes. The continuous-time case focuses on Harris recurrent diffusion processes. Notwithstanding finite-sample adjustments discussed in the paper, the proposed tests are simple to implement and rely on tabulated critical values. Simulations show that their size and power properties are satisfactory. Our robustness to nonlinear dynamics provides a solution to the typical inconsistency problem between assumed linearity of a time series for the purpose of nonstationarity testing and subsequent nonlinear inference.

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42

Meyn, Sean P., and R. L. Tweedie. "Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes." Advances in Applied Probability 25, no. 03 (September 1993): 518–48. http://dx.doi.org/10.1017/s0001867800025532.

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In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator. Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula. We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion for f-norm convergence, and bounding constants for such convergence in the exponential ergodic case. We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.

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43

Meyn, Sean P., and R. L. Tweedie. "Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes." Advances in Applied Probability 25, no. 3 (September 1993): 518–48. http://dx.doi.org/10.2307/1427522.

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In Part I we developed stability concepts for discrete chains, together with Foster–Lyapunov criteria for them to hold. Part II was devoted to developing related stability concepts for continuous-time processes. In this paper we develop criteria for these forms of stability for continuous-parameter Markovian processes on general state spaces, based on Foster-Lyapunov inequalities for the extended generator.Such test function criteria are found for non-explosivity, non-evanescence, Harris recurrence, and positive Harris recurrence. These results are proved by systematic application of Dynkin's formula.We also strengthen known ergodic theorems, and especially exponential ergodic results, for continuous-time processes. In particular we are able to show that the test function approach provides a criterion for f-norm convergence, and bounding constants for such convergence in the exponential ergodic case.We apply the criteria to several specific processes, including linear stochastic systems under non-linear feedback, work-modulated queues, general release storage processes and risk processes.

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44

Lukinskiy, Valery, and Viktor Dobromirov. "Methods of Evaluating Transportation and Logistics Operations in Supply Chains." Transport and Telecommunication Journal 17, no. 1 (March 1, 2016): 55–59. http://dx.doi.org/10.1515/ttj-2016-0006.

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Abstract The paper considers some issues related to different approaches to estimation of transport and logistic(s) operations in supply networks; analysis is made of the methods and models of analytical description of those operations; it is shown that the works under consideration have no single approach to their accounting, which makes it impossible to form a model of a simple logistic network including such basic operations as transportation and storage; based on the classical model of Harris-Wilson, six versions have been obtained for a simple supply network showing, in particular, value added to the product price stemming from the previously performed logistic operations as well as restrictions associated with the load capacity (cargo capacity) of the vehicle. The choice of an optimum version of the supply network is made based on the criterion of minimum total costs; there are supplied the examples of calculations for different versions of the developed models enabling estimation of the influence of transport and logistic operations on the efficiency of the supply network.

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45

Last, Günter, and Ryszard Szekli. "Asymptotic and monotonicity properties of some repairable systems." Advances in Applied Probability 30, no. 04 (December 1998): 1089–110. http://dx.doi.org/10.1017/s0001867800008818.

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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.

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46

Last, Günter, and Ryszard Szekli. "Asymptotic and monotonicity properties of some repairable systems." Advances in Applied Probability 30, no. 4 (December 1998): 1089–110. http://dx.doi.org/10.1239/aap/1035228209.

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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.

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47

Chen, Xia. "On the limit laws of the second order for additive functionals of Harris recurrent Markov chains." Probability Theory and Related Fields 116, no. 1 (January 2000): 89–123. http://dx.doi.org/10.1007/pl00008724.

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48

King, Martin D., Martin J. Crowder, David J. Hand, Neil G. Harris, Stephen R. Williams, Tihomir P. Obrenovitch, and David G. Gadian. "Temporal Relation between the ADC and DC Potential Responses to Transient Focal Ischemia in the Rat: A Markov Chain Monte Carlo Simulation Analysis." Journal of Cerebral Blood Flow & Metabolism 23, no. 6 (June 2003): 677–88. http://dx.doi.org/10.1097/01.wcb.0000066919.40164.c0.

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Markov chain Monte Carlo simulation was used in a reanalysis of the longitudinal data obtained by Harris et al. ( J Cereb Blood Flow Metab 20:28–36) in a study of the direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischemia. The main purpose was to provide a formal analysis of the temporal relationship between the ADC and DC responses, to explore the possible involvement of a common latent (driving) process. A Bayesian nonlinear hierarchical random coefficients model was adopted. DC and ADC transition parameter posterior probability distributions were generated using three parallel Markov chains created using the Metropolis algorithm. Particular attention was paid to the within-subject differences between the DC and ADC time course characteristics. The results show that the DC response is biphasic, whereas the ADC exhibits monophasic behavior, and that the two DC components are each distinguishable from the ADC response in their time dependencies. The DC and ADC changes are not, therefore, driven by a common latent process. This work demonstrates a general analytical approach to the multivariate, longitudinal data-processing problem that commonly arises in stroke and other biomedical research.

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49

Katsoulakou, Eugenia, Konstantis F. Konidaris, Catherine P. Raptopoulou, Vassilis Psyharis, Evy Manessi-Zoupa, and Spyros P. Perlepes. "Synthesis, X-Ray Structure, and Characterization ofCatena-bis(benzoate)bis{N,N-bis(2-hydroxyethyl)glycinate}cadmium(II)." Bioinorganic Chemistry and Applications 2010 (2010): 1–8. http://dx.doi.org/10.1155/2010/281932.

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The reaction of -bis(2-hydroxyethyl)glycine (bicine; ) with in MeOH yielded the polymeric compound . The complex crystallizes in the tetragonal space group . The lattice constants are and Å. The compound contains chains of repeating units. One atom is coordinated by two carboxylate oxygen, four hydroxyl oxygen, and two nitrogen atoms from two symmetry-related 2.21111 (Harris notation) ligands. The other atom is coordinated by six carboxylate oxygen atoms, four from two ligands and two from the monodentate benzoate groups. Each bicinate(-1) ligand chelates the 8-coordinate, square antiprismatic atom through one carboxylate oxygen, the nitrogen, and both hydroxyl oxygen atoms and bridges the second, six-coordinate trigonal prismatic center through its carboxylate oxygen atoms. Compound1is the first structurally characterized cadmium(II) complex containing any anionic form of bicine as ligand. IR data of1are discussed in terms of the coordination modes of the ligands and the known structure.

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Duchi, John C., Peter W. Glynn, and Hongseok Namkoong. "Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach." Mathematics of Operations Research 46, no. 3 (August 2021): 946–69. http://dx.doi.org/10.1287/moor.2020.1085.

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We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework—based on distributional uncertainty sets constructed from nonparametric f-divergence balls—for Hadamard differentiable functionals, and in particular, stochastic optimization problems. As consequences of this theory, we provide a principled method for choosing the size of distributional uncertainty regions to provide one- and two-sided confidence intervals that achieve exact coverage. We also give an asymptotic expansion for our distributionally robust formulation, showing how robustification regularizes problems by their variance. Finally, we show that optimizers of the distributionally robust formulations we study enjoy (essentially) the same consistency properties as those in classical sample average approximations. Our general approach applies to quickly mixing stationary sequences, including geometrically ergodic Harris recurrent Markov chains.

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Journal articles on the topic 'Harris chains'

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