Electronic Communications in Probability

An Application of Renewal Theorems to Exponential Moments of Local Times

Leif Döring and Mladen Savov

Full-text: Open access

Abstract

In this note we explain two transitions known for moment generating functions of local times by means of properties of the renewal measure of a related renewal equation. The arguments simplify and strengthen results on the asymptotic behavior in the literature

Article information

Source
Electron. Commun. Probab., Volume 15 (2010), paper no. 24, 263-269.

Dates
Accepted: 7 June 2010
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465243967

Digital Object Identifier
doi:10.1214/ECP.v15-1558

Mathematical Reviews number (MathSciNet)
MR2658973

Zentralblatt MATH identifier
1226.60103

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Renewal Theorem Local Times

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Döring, Leif; Savov, Mladen. An Application of Renewal Theorems to Exponential Moments of Local Times. Electron. Commun. Probab. 15 (2010), paper no. 24, 263--269. doi:10.1214/ECP.v15-1558. https://projecteuclid.org/euclid.ecp/1465243967


Export citation

References

  • K.K. Anderson, K.B. Athreya. A Renewal Theorem in the Infinite Mean Case. Annals of Probability. 15 (1987), 388-393.
  • N.H. Bingham, C.M. Goldie, J.L. Teugels. Regular variation. Encyclopedia of Mathematics and its Applications (1989), xx+494.
  • F. Aurzada, L. D?ring. Intermittency and Aging for the Symbiotic Branching Model. to appear in Ann. Inst. H. Poincare Probab. Statist. (2010).
  • R. Carmona, S. Molchanov. Parabolic Anderson problem and intermittency. Mem. Amer. Math. Soc. 108 (1994), viii+125.
  • A. Dembo, J.D. Deuschel. Aging for Interacting Diffusion Processes. Ann. Inst. H. Poincare Probab. Statist. 43(4) (2007), 461-480.
  • B. Erickson. The strong law of large numbers when the mean is undefined. Trans. Amer. Math. Soc. 54 (1973), 371-381.
  • W. Feller. An introduction to probability theory and its applications. Vol. II. John Wiley & Sons, Inc., New York-London-Sydney (1971), xxiv+669 pp.
  • M. Foondun, D. Khoshnevisan. Intermittency for nonlinear parabolic stochastic partial differential equations. Electr. Journal of Prob. 14 (2009), 548-568.
  • M. Foondun, D. Khoshnevisan. On the global maximum of the solution to a stochastic heat equation with compact-support initial data. Preprint.
  • J. G?rtner, F. den Hollander. Intermittency in a catalytic random medium. Annals of Probability 34(6) (2006), 2219-2287.
  • M. Marcus, J. Rosen. Laws of the iterated logarithm for the local times of symmetric Levy processes and recurrent random walks. Annals of Probability 22 (1994), 620-659.