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Volumn 75, Issue 1, 1998, Pages 1-30

Stability results for a general class of interacting point processes dynamics, and applications1

Author keywords

Ergodicity; Hawkes processes; Neuron networks; Point processes; Stationary point processes; Stochastic differential equations; Stochastic intensity

Indexed keywords


EID: 0002294068     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0304-4149(98)00006-4     Document Type: Article
Times cited : (50)

References (23)
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    • Brémaud, P.1    Massoulié, L.2
  • 4
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    • Stability of non linear Hawkes processes
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    • (1996) Ann. Probab. , vol.24 , Issue.3 , pp. 1563-1588
    • Brémaud, P.1    Massoulié, L.2
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    • Metastability in the Greenberg-Hastings model
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    • Fisch, R.1    Gravner, J.2    Griffeath, D.3
  • 9
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    • Thèse de Doctorat. LMC-IMAG, Grenoble, France.
    • Forbes, F., 1996. Thèse de Doctorat. LMC-IMAG, Grenoble, France.
    • (1996)
    • Forbes, F.1
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    • 0011592122 scopus 로고
    • On the representation of integer-valued random measures by means of stochastic integrals with respect to Poisson measure
    • Grigelionis B. On the representation of integer-valued random measures by means of stochastic integrals with respect to Poisson measure. Litovsk. Mat. Sb. 11:1971;93-108.
    • (1971) Litovsk. Mat. Sb. , vol.11 , pp. 93-108
    • Grigelionis, B.1
  • 12
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    • Spectra of some self-exciting and mutually exciting point processes
    • Hawkes A.G. Spectra of some self-exciting and mutually exciting point processes. Biometrika. 58:1971;83-90.
    • (1971) Biometrika , vol.58 , pp. 83-90
    • Hawkes, A.G.1
  • 13
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    • Multivariate point processes: Predictable projections, Radon-Nikodym derivatives, representation of martingales
    • Jacod, J., 1975. Multivariate point processes: Predictable projections, Radon-Nikodym derivatives, representation of martingales. Z. Wahrs. 31, 235-253.
    • (1975) Z. Wahrs. , vol.31 , pp. 235-253
    • Jacod, J.1
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    • Stochastic Models of Computer Communication Systems
    • Kelly F.P. Stochastic Models of Computer Communication Systems. J. Roy. Statist. Soc. B. 85:1985;379-395.
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    • Kelly, F.P.1
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    • Simulation of nonhomogeneous Poisson processes with log linear rate function
    • Lewis P.A.W., Shedler G.S. Simulation of nonhomogeneous Poisson processes with log linear rate function. Biometrika. 63:1976;501-506.
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    • Lewis, P.A.W.1    Shedler, G.S.2
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    • Stability of Markovian Processes II: Continuous time processes and sampled chains
    • Meyn S.P., Tweedie R.L. Stability of Markovian Processes II. continuous time processes and sampled chains Adv. Appl. Probab. 25:1993;487-517.
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    • Meyn, S.P.1    Tweedie, R.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.