Recurrence classification for a family of non-linear storage models

• Autorzy: Glynn, P. W. , Glynn, J. E. , Rai, S.
• Języki publikacji: EN

Abstrakty

EN

Necessary and sufficient conditions for positive recurrence of a discrete-time non-linear storage model with power law dynamics are derived. In addition, necessary and sufficient conditions for finiteness of p-th stationary moments are obtained for this class of models.

Słowa kluczowe

EN

Markov chains; storage theory; positive recurrence; Lyapunov functions

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2017
• Tom: Vol. 37, Fasc. 2
• Strony: 337--353
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Glynn, P. W.

• Dept. of Management Science and Engineering, Stanford University, Stanford, CA, 94305, U.S.,

autor

Glynn, J. E.

• Ottawa,

autor

Rai, S.

• Man Group, London, U.K.,

Bibliografia

• [1] K. B. Athreya and S. G. Pantula, Mixing properties of Harris chains and autoregressive processes, J. Appl. Probab. 23 (4) (1986), pp. 880-892.
• [2] L. Breiman, Probability, Addison-Wesley, Reading, MA, 1968.
• [3] P. J. Brockwell, S. I. Resnick, and R. L. Tweedie, Storage processes with general release rule and additive inputs, Adv. in Appl. Probab. 14 (2) (1982), pp. 392-433.
• [4] E. P. Campbell and B. C. Bates, Regionalization of rainfall-runoff model parameters using Markov Chain Monte Carlo samples, Water Resour. Res. 37 (3) (2001), pp. 731-739.
• [5] D. J. Daley and T. Rolski, Finiteness of waiting-time moments in general stationary single-server queues, Ann. Appl. Probab. 2 (4) (1992), pp. 987-1008.
• [6] D. J. Daley and T. Rolski, Light traffic approximations in general stationary single-server queues, Stochastic Process. Appl. 49 (1) (1994), pp. 141-158.
• [7] J. L. Doob, Stochastic Processes, Wiley, New York 1953.
• [8] J. E. Glynn, A discrete-time storage process with a general release rule, J. Appl. Probab. 26 (3) (1989), pp. 566-583.
• [9] J. E. Glynn and P. W. Glynn, A diffusion approximation for a network of reservoirs with power law release rule, Stochastic Hydrol. Hydraul. 10 (1) (1996), pp. 17-37.
• [10] P. W. Glynn and A. Zeevi, Recurrence properties of autoregressive processes with superheavy-tailed innovations, J. Appl. Probab. 41 (3) (2004), pp. 639-653.
• [11] J. M. Harrison and S. I. Resnick, The recurrence classification of risk and storage processes, Math. Oper. Res. 3 (1) (1978), pp. 57-66.
• [12] J. Kiefer and J. Wolfowitz, On the characteristics of the general queueing process, with applications to the random walk, Ann. Math. Stat. 27 (1) (1956), pp. 147-161.
• [13] V. Klemes, Physically based stochastic hydrologic analysis, Adv. Hydrosci. 11 (1978), pp. 285-356.
• [14] M. Mandjes, Z. Palmowski, and T. Rolski, Quasi-stationary workload in a Lévy-driven storage system, Stoch. Models 28 (3) (2012), pp. 413-432.
• [15] S. P. Meyn and R. L. Tweedie, Markov Chains and Stochastic Stability, Springer, London 1993.
• [16] Z. Palmowski and T. Rolski, A technique for exponential change of measure for Markov processes, Bernoulli 8 (6) (2002), pp. 767-785.
• [17] Z. Palmowski and T. Rolski, Markov processes conditioned to never exit a subspace of the state space, Probab. Math. Statist. 24 (2) (2004), pp. 339-354.
• [18] Z. Palmowski and T. Rolski, On the exact asymptotics of the busy period in GI/G/1 queues, Adv. in Appl. Probab. 38 (3) (2006), pp. 792-803.
• [19] M. Polak and T. Rolski, A note on speed of convergence to the quasi-stationary distribution, Demonstr. Math. 45 (2) (2012), pp. 385-397.
• [20] W. T. Sloan, A physics-based function for modeling transient groundwater discharge at the watershed scale, Water Resour. Res. 36 (1) (2000), pp. 225-241.
• [21] C. T. Wang, V. K. Gupta, and E. Waymire, A geomorphologic synthesis of nonlinearity in surface runoff, Water Resour. Res. 17 (3) (1981), pp. 545-554.

Uwagi

Dedicated to Professor Tomasz Rolski on the occasion of his 70th birthday.

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).

Identyfikatory

DOI

10.19195/0208-4147.37.2.8