Tempered stable laws as random walk limits

Preprint English OPEN
Chakrabarty, Arijit; Meerschaert, Mark M.;
  • Subject: Mathematics - Probability

Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered ... View more
  • References (18)
    18 references, page 1 of 2

    Aban, I., Meerschaert, M., and Panorska, A. (2006). Parameter estimation for the truncated Pareto distribution. Journal of the American Statistical Association, 101(473):270-277.

    Baeumer, B. and Meerschaert, M. M. (2010). Tempered stable L´evy motion and transient super-diffusion. Journal of Computational and Applied Mathematics, 233:243- 2448.

    Billingsley, P. (1968). Convergence of Probability Measures. Wiley, New York.

    Carr, P., Geman, H., Madan, D. B., and Yor, M. (2002). The fine structure of asset returns: An empirical investigation. J. Business, 75:303-325.

    Carr, P., Geman, H., Madan, D. B., and Yor, M. (2003). Stochastic volatility for l´evy processes. Math. Finance, 13:345-382.

    Koponen, I. (1995). Analytic approach to the problem of convergence of truncated l´evy flights towards the gaussian stochastic process. Phys. Rev. E, 52:1197-1199.

    Meerschaert, M. M., Benson, D. A., and Baeumer, B. (1999). Multidimensional advection and fractional dispersion. Phys. Rev. E, 59:5026-5028.

    Meerschaert, M. M., Roy, P., and Shao, Q. (2010). Parameter estimation for tempered power law distributions. Communications in Statistics - Theory and Methods, to appear. Preprint available at www.stt.msu.edu/~mcubed/TempPareto.pdf.

    Meerschaert, M. M. and Scheffler, H.-P. (2001). Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. Wiley, New York.

    Meerschaert, M. M. and Scheffler, H.-P. (2004). Limit theorems for continuous time random walks with infinite mean waiting times. Journal of Applied Probability, 41:623-638.

  • Metrics
    No metrics available