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Almost sure path properties of Branching Diffusion Processes

Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1686)

Abstract

We consider a one-dimensional Branching Brownian Motion. We present a large deviations result concerning the almost sure number of particles along any given path. We then observe the implications of this result by studying Branching Integrated Brownian Motion.

Key Words

  • Strassen Law
  • Large Deviations
  • Branching Diffusion Processes
  • Reaction Diffusion Equations

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References

  1. Chauvin, B. & Rouault, A. KPP equation and branching Brownian Motion in the subcritical speed-area. Application to spatial trees. Prob. Th. and Rel. Fields 80, 1988. p299–314.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Neveu, J. Multiplicative martingales for spatial branching process. Sem. Stochastic Processes Princeton. p223–242.

    Google Scholar 

  3. Schilder, M. Some Asymptotic formulae for Wiener integrals. Trans. Amer. Math. Soc. 125, 1966. p63–85

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. Strassen, V. An invariance principle for the law of the iterated logarithm. Z. Wahrsch. Verw. Gebiete 3, 1964. p227–246.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. Uchiyama, K. Spatial growth of a branching process of particles living ind. Annals of Probability 10, 1982. p896–918.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Varadhan, S.R.S. Large Deviations and Applications. CBMS-NSF Regional Conference Series in Applied Mathematics, 1984.

    Google Scholar 

  7. Warren, J. Some Aspects of Branching Processes. Ph.D. dissertation, University of Bath, 1995

    Google Scholar 

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© 1998 Springer-Verlag

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Git, Y. (1998). Almost sure path properties of Branching Diffusion Processes. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds) Séminaire de Probabilités XXXII. Lecture Notes in Mathematics, vol 1686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101754

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  • DOI: https://doi.org/10.1007/BFb0101754

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64376-0

  • Online ISBN: 978-3-540-69762-6

  • eBook Packages: Springer Book Archive