메뉴 건너뛰기




Volumn 24, Issue 2, 1996, Pages 916-931

A liapounov bound for solutions of the poisson equation

Author keywords

Foster's criterion; Functional central limit theorem; Liapounov function; Markov chain; Markov process; Perturbation theory; Poisson equation

Indexed keywords


EID: 0030522182     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1039639370     Document Type: Article
Times cited : (203)

References (36)
  • 3
    • 0022863898 scopus 로고
    • Mixing properties of Harris chains and autoregressive processes
    • ATHREYA, K. B. and PANTULA, S. G. (1986). Mixing properties of Harris chains and autoregressive processes. J. Appl. Probab. 23 880-892.
    • (1986) J. Appl. Probab. , vol.23 , pp. 880-892
    • Athreya, K.B.1    Pantula, S.G.2
  • 5
    • 0040125256 scopus 로고
    • On the functional central limit theorem and the law of the iterated logarithm for Markov processes
    • BHATTACHARAYA, R. N. (1982). On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Z. Wahrsch. Verw. Gebiete 60 185-201.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.60 , pp. 185-201
    • Bhattacharaya, R.N.1
  • 9
    • 0040553088 scopus 로고
    • Geometric and uniform ergodicity of Markov processes
    • To appear
    • DOWN, D., MEYN, S. P. and TWEEDIE, R. L. (1993). Geometric and uniform ergodicity of Markov processes. Ann. Probab. To appear.
    • (1993) Ann. Probab.
    • Down, D.1    Meyn, S.P.2    Tweedie, R.L.3
  • 12
    • 0010922921 scopus 로고
    • Poisson's equation for the recurrent M/G/1 queue
    • GLYNN, P. W. (1994). Poisson's equation for the recurrent M/G/1 queue. Adv. in Appl. Probab. 26 1044-1062.
    • (1994) Adv. in Appl. Probab. , vol.26 , pp. 1044-1062
    • Glynn, P.W.1
  • 14
    • 0029250558 scopus 로고
    • Stability of queueing networks and scheduling policies
    • KUMAR, P. R. and MEYN, S. P. (1995). Stability of queueing networks and scheduling policies IEEE Trans. Automat. Control 40 251-260.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 251-260
    • Kumar, P.R.1    Meyn, S.P.2
  • 15
    • 0039960072 scopus 로고
    • The central limit theorem for Markov chains
    • KURTZ, T. G. (1981). The central limit theorem for Markov chains. Ann. Probab. 9 557-560.
    • (1981) Ann. Probab. , vol.9 , pp. 557-560
    • Kurtz, T.G.1
  • 17
    • 0001583850 scopus 로고
    • Théorème de limite centrale pour une chaine de Markov récurrente Harris positive
    • MAIGRET, N. (1978). Théorème de limite centrale pour une chaine de Markov récurrente Harris positive. Ann. Inst. H. Poincaré Probab. Statist. 14 425-440.
    • (1978) Ann. Inst. H. Poincaré Probab. Statist. , vol.14 , pp. 425-440
    • Maigret, N.1
  • 18
    • 0026953213 scopus 로고
    • Stochastic approximations and adaptive control of a discrete-time single-server network with random routing
    • MAKOWSKI, A. and SHWARTZ, A. (1992). Stochastic approximations and adaptive control of a discrete-time single-server network with random routing. SIAM J. Control Optim. 30.
    • (1992) SIAM J. Control Optim. , vol.30
    • Makowski, A.1    Shwartz, A.2
  • 19
    • 0013198589 scopus 로고
    • Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques a pas décroissants
    • METIVIER, M. and PRIOURET, P. (1987). Théorèmes de convergence presque sure pour une classe d'algorithmes stochastiques a pas décroissants. Probab. Theory Related Fields 74 403-428.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 403-428
    • Metivier, M.1    Priouret, P.2
  • 20
    • 0001695753 scopus 로고
    • Stability of generalized Jackson networks
    • MEYN, S. P. and DOWN, D. (1994). Stability of generalized Jackson networks. Ann. Appl. Probab. 4 124-148.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 124-148
    • Meyn, S.P.1    Down, D.2
  • 21
    • 0026854642 scopus 로고
    • Stability, convergence, and performance of an adaptive control algorithm applied to a randomly varying system
    • MEYN, S. P. and GUO, L. (1992). Stability, convergence, and performance of an adaptive control algorithm applied to a randomly varying system. IEEE Trans. Automat. Control 37 535-540.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 535-540
    • Meyn, S.P.1    Guo, L.2
  • 22
    • 0005632477 scopus 로고
    • Geometric ergodicity of a bilinear time series model
    • MEYN, S. P. and GUO, L. (1993). Geometric ergodicity of a bilinear time series model. J. Time Ser. Anal. 14 93-108.
    • (1993) J. Time Ser. Anal. , vol.14 , pp. 93-108
    • Meyn, S.P.1    Guo, L.2
  • 23
    • 0001340189 scopus 로고
    • Stability of Markovian processes I. Discrete time chains
    • MEYN, S. P. and TWEEDIE, R. L. (1992). Stability of Markovian processes I. Discrete time chains. Adv. in Appl. Probab. 24 542-574.
    • (1992) Adv. in Appl. Probab. , vol.24 , pp. 542-574
    • Meyn, S.P.1    Tweedie, R.L.2
  • 24
    • 0009089457 scopus 로고
    • Generalized resolvents and Harris recurrence of Markov processes
    • MEYN, S. P. and TWEEDIE, R. L. (1993). Generalized resolvents and Harris recurrence of Markov processes. Contemp. Math. 149 227-250.
    • (1993) Contemp. Math. , vol.149 , pp. 227-250
    • Meyn, S.P.1    Tweedie, R.L.2
  • 26
    • 0000684659 scopus 로고
    • Stability of Markovian processes II. Continuous time processes and sampled chains
    • MEYN, S. P. and TWEEDIE, R. L. (1993). Stability of Markovian processes II. Continuous time processes and sampled chains. Adv. in Appl. Probab. 25 487-517.
    • (1993) Adv. in Appl. Probab. , vol.25 , pp. 487-517
    • Meyn, S.P.1    Tweedie, R.L.2
  • 27
    • 0001340188 scopus 로고
    • Stability of Markovian processes III. Foster-Lyapunov criteria for continuous time processes
    • MEYN, S. P. and TWEEDIE, R. L. (1993). Stability of Markovian processes III. Foster-Lyapunov criteria for continuous time processes. Adv. in Appl. Probab. 25 518-548.
    • (1993) Adv. in Appl. Probab. , vol.25 , pp. 518-548
    • Meyn, S.P.1    Tweedie, R.L.2
  • 28
    • 0010129277 scopus 로고
    • Potentiel Markovien récurrent des chaînes de Harris
    • NEVEU, J. (1972). Potentiel Markovien récurrent des chaînes de Harris. Ann. Inst. Fourier (Grenoble) 22 7-130.
    • (1972) Ann. Inst. Fourier (Grenoble) , vol.22 , pp. 7-130
    • Neveu, J.1
  • 30
    • 0039367797 scopus 로고
    • On the Poisson equation in the potential theory of a single kernel
    • NUMMELIN, E. (1991). On the Poisson equation in the potential theory of a single kernel. Math. Scand. 68 59-82.
    • (1991) Math. Scand. , vol.68 , pp. 59-82
    • Nummelin, E.1
  • 31
    • 0000099991 scopus 로고
    • Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory
    • NUMMELIN, E. and TUOMINEN, P. (1982). Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory. Stochastic Process Appl. 12 187-202.
    • (1982) Stochastic Process Appl. , vol.12 , pp. 187-202
    • Nummelin, E.1    Tuominen, P.2
  • 34
    • 0001296683 scopus 로고
    • Perturbation theory and finite Markov chains
    • SCHWEITZER, P. J. (1968). Perturbation theory and finite Markov chains. J. Appl. Probab. 5 401-403.
    • (1968) J. Appl. Probab. , vol.5 , pp. 401-403
    • Schweitzer, P.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.