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A nuclear space-valued stochastic differential equation driven by poisson random measures

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Stochastic Partial Differential Equations and Their Applications

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 176))

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References

  1. C.Dellacherie & P.A.Meyer, Probabilities and Potential B, North-Holland, 1982.

    Google Scholar 

  2. I. Gyöngy, On stochastic equation with respect to semimartingales III; Stochastics, Vol 7, pp.231–245, 1982.

    Google Scholar 

  3. I. Gyöngy and N.V. Krylov, On stochastic equation with respect to semimartingales I; Stochastics, Vol 4, pp.1–21, 1980.

    Google Scholar 

  4. G.Hardy, G.Kallianpur and S.Ramasubramanian, A nuclear space-valued stochastic differential equation driven by Poisson random measures; University of North Carolina at Chapel Hill Technical report No. 232.

    Google Scholar 

  5. M. Hitsuda and I. Mitoma, Tightness problem and stochastic evolution equation arising from fluctuation phenomena for interacting diffusions, J. Multivariate Analysis 19, pp.311–328,1986.

    Google Scholar 

  6. N.Ikeda and S.Watanabe, Stochastic differential equations and diffusion processes; North-Holland, 1981.

    Google Scholar 

  7. K.Itô, Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces, Society for Industrial and Applied Mathematics, 1984.

    Google Scholar 

  8. J. Jacod and A.N. Shiryaev, Limit theorem for stochastic processes; Springer-Verlag, 1987.

    Google Scholar 

  9. G.Kallianpur, Stochastic differential equations in duals of nuclear spaces with some applications, University of North Carolina at Chapel Hill Technical Report No. 158.

    Google Scholar 

  10. G. Kallianpur, I. Mitoma and R.L. Wolpert, Diffusion equation in duals of nuclear spaces; Stochastics and stochastic reports, Vol 29, pp.285–329, 1990.

    Google Scholar 

  11. G. Kallianpur and R.L. Wolpert, Infinite dimensional stochastic differential equation models for spatially distributed neuron, Appl. math. optim. 12, pp.125–172, 1984.

    Google Scholar 

  12. G.Kallianpur and R.L.Wolpert, Weak convergence of stochastic neuronal models, Lecture Notes in Biomathematic, Eds. M.Kimura, G.Kallianpur and T.Hida, Stochastic Methods in Biology, pp116–145.

    Google Scholar 

  13. P.Kotelenez, Gaussian approximation to the nonlinear reaction-diffusion equation, Report No. 146, University of Bremen, 1986.

    Google Scholar 

  14. N.Krylov and B.Rozovskii, Stochastic Evolution Equations, Plenum Publishing Corporation, pp.1233–1277, 1981.

    Google Scholar 

  15. I. Mitoma, Tightness of probabilities on C([0,1],φ′) and D([0,1],φ′); The Annals of Probability, Vol. 11, No 4, pp.989–999, 1983.

    Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, University of North Carolina, Chapel Hill

    G. Kallianpur & J. Xiong

Authors
  1. G. Kallianpur
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  2. J. Xiong
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Boris L. Rozovskii Richard B. Sowers

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© 1992 International Federation for Information Processing

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Kallianpur, G., Xiong, J. (1992). A nuclear space-valued stochastic differential equation driven by poisson random measures. In: Rozovskii, B.L., Sowers, R.B. (eds) Stochastic Partial Differential Equations and Their Applications. Lecture Notes in Control and Information Sciences, vol 176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007328

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  • DOI: https://doi.org/10.1007/BFb0007328

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55292-5

  • Online ISBN: 978-3-540-47015-1

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