메뉴 건너뛰기




Volumn 56, Issue 5, 2001, Pages 803-916

Large deviations for Markov chains in the positive quadrant

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0040927638     PISSN: 00360279     EISSN: 14684829     Source Type: Journal    
DOI: 10.1070/RM2001v056n05ABEH000398     Document Type: Article
Times cited : (42)

References (62)
  • 2
    • 0033229186 scopus 로고    scopus 로고
    • Large deviations analysis of the generalized processor sharing policy
    • D. Bertsimas, I. Paschalidis, and J. Tsitsiklis, "Large deviations analysis of the generalized processor sharing policy", Queueing Systems 32 (1999), 319-349.
    • (1999) Queueing Systems , vol.32 , pp. 319-349
    • Bertsimas, D.1    Paschalidis, I.2    Tsitsiklis, J.3
  • 3
    • 0001768620 scopus 로고
    • Process level large deviations for a class of piecewise homogeneous random walks
    • (M. I. Freidlin, ed.), Birkhäuser, Boston
    • V. M. Blinovskij and R. L. Dobrushin, "Process level large deviations for a class of piecewise homogeneous random walks", The Dynkin Festschrift: Markov Processes and their Applications (M. I. Freidlin, ed.), Birkhäuser, Boston 1994, pp. 1-59.
    • (1994) The Dynkin Festschrift: Markov Processes and Their Applications , pp. 1-59
    • Blinovskij, V.M.1    Dobrushin, R.L.2
  • 5
    • 0004222929 scopus 로고    scopus 로고
    • Editorial URSS, Moscow English transl., Gordon and Breach, New York 1998
    • A. A. Borovkov, Probability theory, Editorial URSS, Moscow 1999; English transl., Gordon and Breach, New York 1998.
    • (1999) Probability Theory
    • Borovkov, A.A.1
  • 6
    • 0040852864 scopus 로고
    • New limit theorems in boundary problems for sums of independent terms
    • A. A. Borovkov, "New limit theorems in boundary problems for sums of independent terms", Sibirsk. Math. Zh. 3 (1962), 645-694; English transl., Select. Transl. Math. Stat. Probab. 5 (1965), 315-372.
    • (1962) Sibirsk. Math. Zh. , vol.3 , pp. 645-694
    • Borovkov, A.A.1
  • 7
    • 0009969734 scopus 로고
    • English transl.
    • A. A. Borovkov, "New limit theorems in boundary problems for sums of independent terms", Sibirsk. Math. Zh. 3 (1962), 645-694; English transl., Select. Transl. Math. Stat. Probab. 5 (1965), 315-372.
    • (1965) Select. Transl. Math. Stat. Probab. , vol.5 , pp. 315-372
  • 8
    • 0040986298 scopus 로고
    • On the Cramér transormation, large deviations in boundary-value problems, and the conditional invariance principle
    • A. A. Borovkov, "On the Cramér transormation, large deviations in boundary-value problems, and the conditional invariance principle", Sibirsk. Math. Zh. 36 (1995), 493-509; English transl., Siberian Math. J. 36 (1995), 417-434.
    • (1995) Sibirsk. Math. Zh. , vol.36 , pp. 493-509
    • Borovkov, A.A.1
  • 9
    • 0000971593 scopus 로고
    • English transl.
    • A. A. Borovkov, "On the Cramér transormation, large deviations in boundary-value problems, and the conditional invariance principle", Sibirsk. Math. Zh. 36 (1995), 493-509; English transl., Siberian Math. J. 36 (1995), 417-434.
    • (1995) Siberian Math. J. , vol.36 , pp. 417-434
  • 10
    • 21444436966 scopus 로고    scopus 로고
    • On the limit conditional distributions connected with large deviations
    • A. A. Borovkov, "On the limit conditional distributions connected with large deviations", Sibirsk. Math. Zh. 37 (1996), 732-744; English transl., Siberian Math. J. 37 (1996), 635-646.
    • (1996) Sibirsk. Math. Zh. , vol.37 , pp. 732-744
    • Borovkov, A.A.1
  • 11
    • 21444436966 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov, "On the limit conditional distributions connected with large deviations", Sibirsk. Math. Zh. 37 (1996), 732-744; English transl., Siberian Math. J. 37 (1996), 635-646.
    • (1996) Siberian Math. J. , vol.37 , pp. 635-646
  • 12
    • 0040397506 scopus 로고
    • Convergence of measures and random processes
    • A. A. Borovkov, "Convergence of measures and random processes", Uspekhi Mat. Nauk 31:2 (1976), 1-69; English transl., Russian Math. Surveys 31:2 (1976), 1-69.
    • (1976) Uspekhi Mat. Nauk , vol.31 , Issue.2 , pp. 1-69
    • Borovkov, A.A.1
  • 13
    • 0039805057 scopus 로고
    • English transl.
    • A. A. Borovkov, "Convergence of measures and random processes", Uspekhi Mat. Nauk 31:2 (1976), 1-69; English transl., Russian Math. Surveys 31:2 (1976), 1-69.
    • (1976) Russian Math. Surveys , vol.31 , Issue.2 , pp. 1-69
  • 14
    • 0010184001 scopus 로고
    • Boundary-value problems for random walks and large deviations in function spaces
    • A. A. Borovkov, "Boundary-value problems for random walks and large deviations in function spaces", Teor. Veroyatnost. i Primenen. 12 (1967), 635-654; English transl., Theory Probab. Appl. 12 (1967), 575-595.
    • (1967) Teor. Veroyatnost. i Primenen. , vol.12 , pp. 635-654
    • Borovkov, A.A.1
  • 15
    • 0010184001 scopus 로고
    • English transl.
    • A. A. Borovkov, "Boundary-value problems for random walks and large deviations in function spaces", Teor. Veroyatnost. i Primenen. 12 (1967), 635-654; English transl., Theory Probab. Appl. 12 (1967), 575-595.
    • (1967) Theory Probab. Appl. , vol.12 , pp. 575-595
  • 16
    • 0040397492 scopus 로고    scopus 로고
    • Large deviation probabilities for one-dimensional Markov chains. I: Stationary distributions
    • A. A. Borovkov and D. A. Korshunov, "Large deviation probabilities for one-dimensional Markov chains. I: Stationary distributions", Teor. Veroyatnost. i Primenen. 41 (1996), 3-30; English transl., Theory Probab. Appl. 41 (1996), 1-24.
    • (1996) Teor. Veroyatnost. i Primenen. , vol.41 , pp. 3-30
    • Borovkov, A.A.1    Korshunov, D.A.2
  • 17
    • 85164648745 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov and D. A. Korshunov, "Large deviation probabilities for one-dimensional Markov chains. I: Stationary distributions", Teor. Veroyatnost. i Primenen. 41 (1996), 3-30; English transl., Theory Probab. Appl. 41 (1996), 1-24.
    • (1996) Theory Probab. Appl. , vol.41 , pp. 1-24
  • 18
    • 0039805035 scopus 로고    scopus 로고
    • Large deviation probabilities for one-dimensional Markov chains. II
    • A. A. Borovkov and D. A. Korshunov, "Large deviation probabilities for one-dimensional Markov chains. II", Teor. Veroyatnost. i Primenen. 45 (2000), 437-468; English transl. in Theory Probab. Appl. 45 (2000).
    • (2000) Teor. Veroyatnost. i Primenen. , vol.45 , pp. 437-468
    • Borovkov, A.A.1    Korshunov, D.A.2
  • 19
    • 85164649931 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov and D. A. Korshunov, "Large deviation probabilities for one-dimensional Markov chains. II", Teor. Veroyatnost. i Primenen. 45 (2000), 437-468; English transl. in Theory Probab. Appl. 45 (2000).
    • (2000) Theory Probab. Appl. , vol.45
  • 20
    • 0032235942 scopus 로고    scopus 로고
    • Integro-local limit theorems including large deviations for sums of random vectors. I
    • A. A. Borovkov and A. A. Mogul'skii, "Integro-local limit theorems including large deviations for sums of random vectors. I", Teor. Veroyatnost. i Primenen. 43 (1998), 3-17; English transl., Theory Probab. Appl. 43 (1998), 1-12.
    • (1998) Teor. Veroyatnost. i Primenen. , vol.43 , pp. 3-17
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 21
    • 85164649592 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov and A. A. Mogul'skii, "Integro-local limit theorems including large deviations for sums of random vectors. I", Teor. Veroyatnost. i Primenen. 43 (1998), 3-17; English transl., Theory Probab. Appl. 43 (1998), 1-12.
    • (1998) Theory Probab. Appl. , vol.43 , pp. 1-12
  • 22
    • 0034562538 scopus 로고    scopus 로고
    • Integro-local limit theorems including large deviations for sums of random vectors. II
    • A. A. Borovkov and A. A. Mogul'skii, "Integro-local limit theorems including large deviations for sums of random vectors. II", Teor. Veroyatnost. i Primenen. 45 (2000), 5-19; English transl., Theory Probab. Appl. 45 (2000), 3-22.
    • (2000) Teor. Veroyatnost. i Primenen. , vol.45 , pp. 5-19
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 23
    • 0039213028 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov and A. A. Mogul'skii, "Integro-local limit theorems including large deviations for sums of random vectors. II", Teor. Veroyatnost. i Primenen. 45 (2000), 5-19; English transl., Theory Probab. Appl. 45 (2000), 3-22.
    • (2000) Theory Probab. Appl. , vol.45 , pp. 3-22
  • 24
    • 0039587837 scopus 로고
    • Large deviations and test of a statistical hypothesis
    • A. A. Borovkov and A. A. Mogul'skii, "Large deviations and test of a statistical hypothesis", Trudy Inst. Mat. 19 (1992); English transl., Siberian Adv. Math. 2:3, 4 (1992); 3:1, 2 (1993).
    • (1992) Trudy Inst. Mat. , vol.19
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 25
    • 5244222744 scopus 로고
    • English transl.
    • A. A. Borovkov and A. A. Mogul'skii, "Large deviations and test of a statistical hypothesis", Trudy Inst. Mat. 19 (1992); English transl., Siberian Adv. Math. 2:3, 4 (1992); 3:1, 2 (1993).
    • (1992) Siberian Adv. Math. , vol.2 , Issue.3 , pp. 4
  • 26
    • 5244220735 scopus 로고
    • A. A. Borovkov and A. A. Mogul'skii, "Large deviations and test of a statistical hypothesis", Trudy Inst. Mat. 19 (1992); English transl., Siberian Adv. Math. 2:3, 4 (1992); 3:1, 2 (1993).
    • (1993) Siberian Adv. Math. , vol.3 , Issue.1 , pp. 2
  • 27
    • 21444437162 scopus 로고    scopus 로고
    • The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks
    • A. A. Borovkov and A. A. Mogul'skii, "The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks", Sibirsk. Math. Zh. 37 (1996), 745-782; English transl., Siberian Math. J. 37 (1996), 647-682.
    • (1996) Sibirsk. Math. Zh. , vol.37 , pp. 745-782
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 28
    • 21444437162 scopus 로고    scopus 로고
    • English transl.
    • A. A. Borovkov and A. A. Mogul'skii, "The second rate function and the asymptotic problems of renewal and hitting the boundary for multidimensional random walks", Sibirsk. Math. Zh. 37 (1996), 745-782; English transl., Siberian Math. J. 37 (1996), 647-682.
    • (1996) Siberian Math. J. , vol.37 , pp. 647-682
  • 29
    • 85164640818 scopus 로고
    • Large deviations for stationary Markov chains in a quarter plane
    • Abstracts of communications, World Scientific, Singapore
    • A. A. Borovkov and A. A. Mogul'skii, "Large deviations for stationary Markov chains in a quarter plane", Abstracts of communications, 23rd Conference on Stochastic Processes and their Applications, World Scientific, Singapore, 1995.
    • (1995) 23rd Conference on Stochastic Processes and Their Applications
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 30
    • 0039213023 scopus 로고    scopus 로고
    • Large deviations for stationary Markov chains in a quarter plane
    • (Tokyo, July 26-30, 1995) (S. Watanabe et al., ed.), World Scientific, Singapore
    • A. A. Borovkov and A. A. Mogul'skii, "Large deviations for stationary Markov chains in a quarter plane", Proc. 7th Japan-Russia Symposium on Probability Theory and Mathematical Statistics (Tokyo, July 26-30, 1995) (S. Watanabe et al., ed.), World Scientific, Singapore, 1996, pp. 12-19.
    • (1996) Proc. 7th Japan-Russia Symposium on Probability Theory and Mathematical Statistics , pp. 12-19
    • Borovkov, A.A.1    Mogul'skii, A.A.2
  • 32
    • 85164646510 scopus 로고
    • English transl., [Probability theory, VII], Springer-Verlag, Berlin
    • A. A. Borovkov, A. A. Mogul'skii, and A. A. Sakhanenko, "Limit theorems for random processes", Itogi Nauki i Tekhniki, Sovrem. Probl. Mat., Fundament. Napravl., vol. 82, VINITI, Moscow 1991; English transl., Encyclopaedia of Math. Sci., vol. 82 [Probability theory, VII], Springer-Verlag, Berlin 1995, pp. 5-199.
    • (1995) Encyclopaedia of Math. Sci. , vol.82 , pp. 5-199
  • 33
    • 0040991536 scopus 로고    scopus 로고
    • Large deviations for random processes with independent increments on infinite intervals
    • (Lectures presented at the semester held in St. Petersburg, March 2 April 23, 1993) (I. A. Ibragimov et al., eds.), Gordon and Breach, Amsterdam
    • R. L. Dobrushin and E. A. Pechersky, "Large deviations for random processes with independent increments on infinite intervals", Probability Theory and Mathematical Statistics (Lectures presented at the semester held in St. Petersburg, March 2 April 23, 1993) (I. A. Ibragimov et al., eds.), Gordon and Breach, Amsterdam 1996, pp. 41-74.
    • (1996) Probability Theory and Mathematical Statistics , pp. 41-74
    • Dobrushin, R.L.1    Pechersky, E.A.2
  • 35
    • 0001470414 scopus 로고
    • Large deviations for Markov processes with discontinuous statistics, II: Random walks
    • P. Dupuis and R. Ellis, "Large deviations for Markov processes with discontinuous statistics, II: Random walks", Probab. Theory Related Fields 91 (1992), 153-194.
    • (1992) Probab. Theory Related Fields , vol.91 , pp. 153-194
    • Dupuis, P.1    Ellis, R.2
  • 36
    • 0000215977 scopus 로고
    • The large deviations principle for a general class of queueing systems. I
    • P. Dupuis and R. Ellis, "The large deviations principle for a general class of queueing systems. I, Trans. Amer. Math. Soc. 348 (1995), 2689-2751.
    • (1995) Trans. Amer. Math. Soc. , vol.348 , pp. 2689-2751
    • Dupuis, P.1    Ellis, R.2
  • 38
    • 0000134614 scopus 로고
    • A viscosing solution approach to the asymptotic analysis of queueing systems
    • P. Dupuis, H. Ishii, and H. M. Soner, "A viscosing solution approach to the asymptotic analysis of queueing systems", Ann. Probab. 18 (1990), 226-255.
    • (1990) Ann. Probab. , vol.18 , pp. 226-255
    • Dupuis, P.1    Ishii, H.2    Soner, H.M.3
  • 40
    • 0030490667 scopus 로고    scopus 로고
    • Stationary tail probabilities in exponential server tandems with renewal arrivals
    • A. Ganesh and V. Anantharam, "Stationary tail probabilities in exponential server tandems with renewal arrivals", Queueing Systems 22 (1996), 203-247.
    • (1996) Queueing Systems , vol.22 , pp. 203-247
    • Ganesh, A.1    Anantharam, V.2
  • 41
    • 0034346718 scopus 로고    scopus 로고
    • Large deviations of a Jackson network
    • I. Ignatiouk-Robert, "Large deviations of a Jackson network", Ann. Appl. Probab. 10 (2000), 962-1001.
    • (2000) Ann. Appl. Probab. , vol.10 , pp. 962-1001
    • Ignatiouk-Robert, I.1
  • 42
    • 0039805028 scopus 로고
    • Boundary effect in large deviation problems
    • I. A. Ignatyuk, V. A. Malyshev, and V. V. Scherbakov, "Boundary effect in large deviation problems", Uspekhi Mat. Nauk 49:2 (1994), 43-102; English transl., Russian Math. Surveys 49:2 (1994), 41-99.
    • (1994) Uspekhi Mat. Nauk , vol.49 , Issue.2 , pp. 43-102
    • Ignatyuk, I.A.1    Malyshev, V.A.2    Scherbakov, V.V.3
  • 43
    • 85164656759 scopus 로고
    • English transl.
    • I. A. Ignatyuk, V. A. Malyshev, and V. V. Scherbakov, "Boundary effect in large deviation problems", Uspekhi Mat. Nauk 49:2 (1994), 43-102; English transl., Russian Math. Surveys 49:2 (1994), 41-99.
    • (1994) Russian Math. Surveys , vol.49 , Issue.2 , pp. 41-99
  • 44
    • 0032377306 scopus 로고    scopus 로고
    • Heavy traffic approximations of large deviations of feedforward queueing networks
    • K. Majewski, "Heavy traffic approximations of large deviations of feedforward queueing networks", Queueing Systems 28 (1998), 125-155.
    • (1998) Queueing Systems , vol.28 , pp. 125-155
    • Majewski, K.1
  • 45
    • 0032339351 scopus 로고    scopus 로고
    • Large deviations on the steady-state distribution of reflected processes with applications to queueing systems
    • K. Majewski, "Large deviations on the steady-state distribution of reflected processes with applications to queueing systems", Queueing Systems 29 (1998), 351-381.
    • (1998) Queueing Systems , vol.29 , pp. 351-381
    • Majewski, K.1
  • 47
    • 85164636028 scopus 로고
    • Probability of large deviations for random walks
    • Russian
    • A. A. Mogul'skii, "Probability of large deviations for random walks", Trudy Inst. Mat. 3 (1983), 93 -121. (Russian)
    • (1983) Trudy Inst. Mat. , vol.3 , pp. 93-121
    • Mogul'skii, A.A.1
  • 48
    • 0001684239 scopus 로고
    • Large deviations for trajectories of multi-dimensional random walks
    • A. A. Mogul'skii, "Large deviations for trajectories of multi-dimensional random walks", Teor. Veroyatnost. i Primenen. 21 (1976), 309-323; English transl., Theory Probab. Appl. 21 (1976), 300-315.
    • (1976) Teor. Veroyatnost. i Primenen. , vol.21 , pp. 309-323
    • Mogul'skii, A.A.1
  • 49
    • 0001684239 scopus 로고
    • English transl.
    • A. A. Mogul'skii, "Large deviations for trajectories of multi-dimensional random walks", Teor. Veroyatnost. i Primenen. 21 (1976), 309-323; English transl., Theory Probab. Appl. 21 (1976), 300-315.
    • (1976) Theory Probab. Appl. , vol.21 , pp. 300-315
  • 50
    • 0002068870 scopus 로고    scopus 로고
    • Random walks in the positive quadrant. I. Local theorems
    • A. A. Mogul'skii and B. A. Rogozin, "Random walks in the positive quadrant. I. Local theorems", Matematicheskie Trudy 2:2 (1999), 57-97; English transl., Siberian Adv. Math. 10:1 (2000), 34-72.
    • (1999) Matematicheskie Trudy , vol.2 , Issue.2 , pp. 57-97
    • Mogul'skii, A.A.1    Rogozin, B.A.2
  • 51
    • 85164647797 scopus 로고    scopus 로고
    • English transl.
    • A. A. Mogul'skii and B. A. Rogozin, "Random walks in the positive quadrant. I. Local theorems", Matematicheskie Trudy 2:2 (1999), 57-97; English transl., Siberian Adv. Math. 10:1 (2000), 34-72.
    • (2000) Siberian Adv. Math. , vol.10 , Issue.1 , pp. 34-72
  • 52
    • 0012406899 scopus 로고    scopus 로고
    • Random walks in the positive quadrant. II. Integral theorems
    • A. A. Mogul'skii and B. A. Rogozin, "Random walks in the positive quadrant. II. Integral theorems", Matematicheskie Trudy 3:1 (2000), 48-118; English transl., Siberian Adv. Math. 10:2 (2000), 35-103.
    • (2000) Matematicheskie Trudy , vol.3 , Issue.1 , pp. 48-118
    • Mogul'skii, A.A.1    Rogozin, B.A.2
  • 53
    • 0040991538 scopus 로고    scopus 로고
    • English transl.
    • A. A. Mogul'skii and B. A. Rogozin, "Random walks in the positive quadrant. II. Integral theorems", Matematicheskie Trudy 3:1 (2000), 48-118; English transl., Siberian Adv. Math. 10:2 (2000), 35-103.
    • (2000) Siberian Adv. Math. , vol.10 , Issue.2 , pp. 35-103
  • 55
    • 0031222942 scopus 로고    scopus 로고
    • Large deviations for departures from a shared buffer
    • N. O'Connell, "Large deviations for departures from a shared buffer", J. Appl. Probab. 34 (1997), 753-766.
    • (1997) J. Appl. Probab. , vol.34 , pp. 753-766
    • O'Connell, N.1
  • 56
    • 0033243599 scopus 로고    scopus 로고
    • Moderate deviations for queues in critical loading
    • A. Puhalskii, "Moderate deviations for queues in critical loading", Queueing Systems 31 (1999), 359-392.
    • (1999) Queueing Systems , vol.31 , pp. 359-392
    • Puhalskii, A.1
  • 58
    • 0001380311 scopus 로고
    • Limit theorems for stochastic processes
    • A. V. Skorokhod, "Limit theorems for stochastic processes", Teor. Veroyatnost. i Primenen. 1 (1956), 289-319; English transl., Theory Probab. Appl. 1 (1956), 261-290.
    • (1956) Teor. Veroyatnost. i Primenen. , vol.1 , pp. 289-319
    • Skorokhod, A.V.1
  • 59
    • 0001380311 scopus 로고
    • English transl.
    • A. V. Skorokhod, "Limit theorems for stochastic processes", Teor. Veroyatnost. i Primenen. 1 (1956), 289-319; English transl., Theory Probab. Appl. 1 (1956), 261-290.
    • (1956) Theory Probab. Appl. , vol.1 , pp. 261-290
  • 60
    • 84981759111 scopus 로고
    • Asymptotic probabilities and differential equations
    • S. R. S. Varadhan, "Asymptotic probabilities and differential equations", Comm. Pure Appl. Math. 19 (1966), 261-286.
    • (1966) Comm. Pure Appl. Math. , vol.19 , pp. 261-286
    • Varadhan, S.R.S.1
  • 62
    • 0039243593 scopus 로고    scopus 로고
    • Rough asymptotics for tandem non-homogeneous M/G/∞ queues via Poissonized empirical processes
    • T. Zajik, "Rough asymptotics for tandem non-homogeneous M/G/∞ queues via Poissonized empirical processes", Queueing Systems 29 (1998), 161-174.
    • (1998) Queueing Systems , vol.29 , pp. 161-174
    • Zajik, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.