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Volumn 40, Issue 2, 2008, Pages 529-547

Boundary behavior and product-from stationary distributions of jump diffusions in the orthant with state-dependent reflections

Author keywords

Diffusion; Jumps; Local time; Product form; Reflection map; Regulator process; Semimartingale; Stationary distribution

Indexed keywords

DIFFUSION; JUMPS; LOCAL TIME; NONNEGATIVE ORTHANT; ORTHANT; PRODUCT FORM; REFLECTION MAP; REGULATOR PROCESS; SEMIMARTINGALE; STATE-DEPENDENT; STATIONARY DISTRIBUTION; STATIONARY DISTRIBUTIONS;

EID: 49349104085     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1214950215     Document Type: Article
Times cited : (7)

References (20)
  • 1
    • 17744373841 scopus 로고
    • Further applications of a general rate conservation law
    • BARDHAN, I. (1995). Further applications of a general rate conservation law. Stoch. Process. Appl. 60, 113-130.
    • (1995) Stoch. Process. Appl , vol.60 , pp. 113-130
    • BARDHAN, I.1
  • 2
    • 33645684371 scopus 로고    scopus 로고
    • Validity of heavy traffic steady state approximations in open queueing networks
    • GAMARNIK, D. AND ZEEVI, A. (2006). Validity of heavy traffic steady state approximations in open queueing networks. Ann. Appl. Prob. 16, 56-90.
    • (2006) Ann. Appl. Prob , vol.16 , pp. 56-90
    • GAMARNIK, D.1    ZEEVI, A.2
  • 3
    • 49349089645 scopus 로고    scopus 로고
    • HARRISON, J. M. (1985). Brownian Motion and Stochastic Flow Systems. John Wiley, New York.
    • HARRISON, J. M. (1985). Brownian Motion and Stochastic Flow Systems. John Wiley, New York.
  • 4
    • 0000585232 scopus 로고
    • Reflected Brownian motion in an orthant
    • HARRISON, J. M. AND REIMAN, M. I. (1981). Reflected Brownian motion in an orthant. Ann. Prob. 9, 302-308.
    • (1981) Ann. Prob , vol.9 , pp. 302-308
    • HARRISON, J.M.1    REIMAN, M.I.2
  • 5
    • 0002500631 scopus 로고
    • Brownian models of open queueing networks with homogeneous customer populations
    • HARRISON, J. AND WILLIAMS, R. J. (1987). Brownian models of open queueing networks with homogeneous customer populations. Stochastics 22, 77-115.
    • (1987) Stochastics , vol.22 , pp. 77-115
    • HARRISON, J.1    WILLIAMS, R.J.2
  • 6
    • 0000193072 scopus 로고
    • Diffusion approximations for queues with server vacations
    • KELLA, O. AND WHITT, W. (1990). Diffusion approximations for queues with server vacations. Adv. Appl. Prob. 22, 706-729.
    • (1990) Adv. Appl. Prob , vol.22 , pp. 706-729
    • KELLA, O.1    WHITT, W.2
  • 8
    • 49349089272 scopus 로고    scopus 로고
    • KUSHNER, H. J. (2001). Heavy Traffic Analysis of Controlled Queueing and Communication Networks (Appl. Math. 47). Springer, New York.
    • KUSHNER, H. J. (2001). Heavy Traffic Analysis of Controlled Queueing and Communication Networks (Appl. Math. 47). Springer, New York.
  • 9
    • 17744368433 scopus 로고    scopus 로고
    • Forward equations for reflected diffusions with jumps
    • MAZUMDAR, R. R. AND GUILLEMIN, F. M. (1996). Forward equations for reflected diffusions with jumps. Appl. Math. Optimization 33, 81-102.
    • (1996) Appl. Math. Optimization , vol.33 , pp. 81-102
    • MAZUMDAR, R.R.1    GUILLEMIN, F.M.2
  • 10
    • 17744388801 scopus 로고    scopus 로고
    • On product-form stationary distributions for reflected diffusions with jumps in the positive orthant
    • PIERA, F., MAZUMDAR, R. AND GUILLEMIN, F. (2005). On product-form stationary distributions for reflected diffusions with jumps in the positive orthant. Adv. Appl. Prob. 37, 212-228.
    • (2005) Adv. Appl. Prob , vol.37 , pp. 212-228
    • PIERA, F.1    MAZUMDAR, R.2    GUILLEMIN, F.3
  • 11
    • 39149127166 scopus 로고    scopus 로고
    • On the local times and boundary properties of reflected diffusions with jumps in the positive orthant
    • PIERA, F., MAZUMDAR, R. AND GUILLEMIN, F. (2006). On the local times and boundary properties of reflected diffusions with jumps in the positive orthant. Markov Process. Relat. Fields 12, 561-582.
    • (2006) Markov Process. Relat. Fields , vol.12 , pp. 561-582
    • PIERA, F.1    MAZUMDAR, R.2    GUILLEMIN, F.3
  • 13
    • 0021481522 scopus 로고    scopus 로고
    • REIMAN, M. I. (1984). Open queueing networks in heavy traffic. Math. Operat. Res. 9, 441-458.
    • REIMAN, M. I. (1984). Open queueing networks in heavy traffic. Math. Operat. Res. 9, 441-458.
  • 14
    • 0002800360 scopus 로고
    • A boundary property of semimartingale reflecting Brownian motions
    • REIMAN, M. I. AND WILLIAMS, R. J. (1988). A boundary property of semimartingale reflecting Brownian motions. Prob. Theory Relat. Fields 77, 87-97.
    • (1988) Prob. Theory Relat. Fields , vol.77 , pp. 87-97
    • REIMAN, M.I.1    WILLIAMS, R.J.2
  • 15
    • 49349101615 scopus 로고    scopus 로고
    • RONG, S. (2000). Reflecting Stochastic Differential Equations with Jumps and Applications (Research Notes Math. 408). Chapman & Hall/CRC, London.
    • RONG, S. (2000). Reflecting Stochastic Differential Equations with Jumps and Applications (Research Notes Math. 408). Chapman & Hall/CRC, London.
  • 16
    • 0036355797 scopus 로고    scopus 로고
    • The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks
    • SHEN, X., CHEN, H., DAI, J. G. AND DAI, W. (2002). The finite element method for computing the stationary distribution of an SRBM in a hypercube with applications to finite buffer queueing networks. Queueing Systems Theory Appl. 42, 33-62.
    • (2002) Queueing Systems Theory Appl , vol.42 , pp. 33-62
    • SHEN, X.1    CHEN, H.2    DAI, J.G.3    DAI, W.4
  • 17
    • 0035435188 scopus 로고    scopus 로고
    • The reflection map with discontinuities
    • WHITT, W. (2001). The reflection map with discontinuities. Math. Operat. Res. 26, 447-484.
    • (2001) Math. Operat. Res , vol.26 , pp. 447-484
    • WHITT, W.1
  • 19
    • 49349109846 scopus 로고    scopus 로고
    • WILLIAMS, R. J. (1995). Semimartingale reflecting Brownian motions in the orthant. In Stochastic Networks (IMA Math. Appl. 71), Springer, New York, pp. 125-137.
    • WILLIAMS, R. J. (1995). Semimartingale reflecting Brownian motions in the orthant. In Stochastic Networks (IMA Vol. Math. Appl. 71), Springer, New York, pp. 125-137.
  • 20
    • 49349083385 scopus 로고    scopus 로고
    • WILLIAMS, R. J. (1998). Reflecting diffusions and queueing networks. In Proceedings of the International Congress of Mathematicians (Berlin, 1998), III, pp. 321-330 (electronic).
    • WILLIAMS, R. J. (1998). Reflecting diffusions and queueing networks. In Proceedings of the International Congress of Mathematicians (Berlin, 1998), Vol. III, pp. 321-330 (electronic).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.