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Exact rates of convergence to the local times of symmetric lévy processes

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Part of the Lecture Notes in Mathematics book series (SEMPROBAB,volume 1583)

Keywords

  • Brownian Motion
  • Local Time
  • Gaussian Process
  • Exact Rate
  • Stationary Increment

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References

  1. N. Bingham, C. Goldie, and J. Teugals, Regular Variation, Cambridge University Press, Cambridge, 1987.

    CrossRef  Google Scholar 

  2. D. Khoshnevisan, Exact rates of convergence to Brownian local time, Preprint.

    Google Scholar 

  3. N. Kono, On the modulous of continuity of sample functions of Gaussian processes, J. Math. Kyoto Univ. 10 (1970), 493–536.

    MATH  Google Scholar 

  4. M.B. Marcus, Holder conditions for Gaussian processes with stationary increments, Trans. Amer. Math. Soc. 134 (1968), 29–52.

    MathSciNet  MATH  Google Scholar 

  5. M.B. Marcus and J. Rosen, Moduli of continuity of local times of strongly symmetric Markov processes via Gaussian processes, J. Theor. Probab. 5 (1992), 791–825.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. -, p-variation of the local times of symmetric stable processes and of Gaussian processes with stationary increments, Ann. Probab. 20 (1992), 1685–1713.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. -, Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes, Ann. Probab. 20 (1992), 1603–1684.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. -, ϕ-variation of the local times of symmetric Levy processes and stationary Gaussian processes, Seminar on Stochastic Processes, 1992 (Boston), Progress in Probability, vol. 33, Birkhauser, Boston, 1993, pp. 209–220.

    MATH  Google Scholar 

  9. E. J. G. Pitman, On the behavior of the characteristic function of a probability distribution in the neighbourhood of the origin, J. Australian Math. Soc. Series A 8 (1968), 422–443.

    CrossRef  MATH  Google Scholar 

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© 1994 Springer-Verlag

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Marcus, M.B., Rosen, J. (1994). Exact rates of convergence to the local times of symmetric lévy processes. In: Azéma, J., Yor, M., Meyer, P.A. (eds) Séminaire de Probabilités XXVIII. Lecture Notes in Mathematics, vol 1583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073837

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  • DOI: https://doi.org/10.1007/BFb0073837

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58331-8

  • Online ISBN: 978-3-540-48656-5

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