$L^1$-Norm of Infinitely Divisible Random Vectors and Certain Stochastic Integrals

Michael B. Marcus (The City College of CUNY)
Jan Rosinski (University of Tennessee)

Abstract


Equivalent upper and lower bounds for the $L^1$ norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 15-29

Publication Date: January 10, 2001

DOI: 10.1214/ECP.v6-1031

References

  1. De la Pena, V.H. and Gine, E. (1999), Decoupling. From dependence to independence. Springer-Verlag, New York. Math. Review 99k:60044
  2. Dunford, N and Schwartz, J.T. (1958), Linear Operators, Part I: General Theory.Decoupling. Wiley, New York. Math. Review 90g:47001a
  3. I.I. Gihman and A.V. Skorohod. (1975), The theory of Stochastic Processes, Vol. 2. Springer, Berlin. Math. Review 51:11656
  4. Klass, M.J. (1980), Precision bounds for the relative error in the approximation of E|S_n| and extensions. Ann. Probab. 8, 350--367. Math. Review 82h:60097
  5. Kwapien, S. and Woyczynski, W.A. (1992), Random Series and Stochastic Integrals: Single and Multiple. Birkh"auser, Boston. Math. Review 94k:60074
  6. Marcus, M.B. and Rosinski, J. Continuity of stochastic integrals with respect to infinitely divisible random measures. 2000 (preprint) Math. Review number not available.
  7. Parthasarathy, K.R. (1967), Probability measures on metric spaces. Academic Press, New York. Math. Review 37:2271
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.