Norming Operators for Operator-Self-Similar Processes

Maejima, Makoto

doi:10.1007/978-1-4612-2030-5_16

Norming Operators for Operator-Self-Similar Processes

Makoto Maejima⁴

Chapter

343 Accesses
3 Citations

Part of the book series: Trends in Mathematics ((TM))

Abstract

There are many similarities between the theory of operator-stable distributions and that of operator-self-similar processes as discussed by Mason [6].

This is a preview of subscription content, log in via an institution.

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

P. Billingsley, Convergence of types in k-spaces, Z. Wahrsch. verw. Gebiete 5 (1966), 175–179.
Article MathSciNet MATH Google Scholar
J.P. Holmes, W.N. Hudson and J.D. Mason, Operator-stable laws: Multiple exponents and elliptical symmetry, Ann. Probab. 10 (1982), 602–612.
Article MathSciNet MATH Google Scholar
W.N. Hudson, Z.J. Jurek and J.A. Veeh, The symmetry group and exponents of operator stable probability measures, Ann. Probab.} 14 (1986), 1014–1023.
Article MathSciNet MATH Google Scholar
W.N. Hudson and J.D. Mason, Operator-self-similar processes in a finite-dimensional space, Trans. Amer. Math. Soc. 273 (1982), 281–297.
Article MathSciNet MATH Google Scholar
R.G. Laha and V.K. Rohatgi, Operator self-similar stochastic processes in R _d, Stoch. Proc. Appl. 12} (1982}), 73–84
Article MathSciNet Google Scholar
J.D. Mason, A comparison of the properties of operator-stable distributions and operator-self-similar processes, Colloquia Mathematicia Societaris Janos Bolya 36 (1982), 751–760.
Google Scholar
M.M. Meerschaert, Regular variation in R ^k, Proc. Amer. Math. Soc. 102 (1988), 341–348.
MathSciNet MATH Google Scholar
M.M. Meerschaert, Norming operators for generalized domain of attraction, J. Theoret. Proab. 7 (1994), 793–798.
Article MathSciNet MATH Google Scholar
J. Michaliček, Der Anziehungsbereich von operator-stabilen Verteilungen im R ₂}, Z. Wahrsch. verw. Gebiete 25 (1972), 57–70.
Article MATH Google Scholar
K. Sato, Self-similar processes with independent increments, Probab. Th. Rel. Fields 89 (1991), 285–300.
Article MATH Google Scholar
M. Sharpe, Operator-stable probability distributions on vector groups, Trans. Amer. Math. Soc. 136 (1969), 51–65.
Article MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics, Keio University, Hiyoshi, Yokohama, 223, Japan
Makoto Maejima

Authors

Makoto Maejima
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Departments of Mathematics & Statistics, Columbia University, New York, NY, 10027-0010, UK
Ioannis Karatzas
Department of Mathematics, University of Tennessee, Knoxville, TN, 37996-1300, USA
Balram S. Rajput
Department of Mathematics, Boston University, Boston, MA, 02215-2411, USA
Murad S. Taqqu

Rights and permissions

Reprints and permissions

Copyright information

About this chapter

Cite this chapter

Maejima, M. (1998). Norming Operators for Operator-Self-Similar Processes. In: Karatzas, I., Rajput, B.S., Taqqu, M.S. (eds) Stochastic Processes and Related Topics. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2030-5_16

Download citation

DOI: https://doi.org/10.1007/978-1-4612-2030-5_16
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7389-9
Online ISBN: 978-1-4612-2030-5
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics