Electronic Communications in Probability

A renewal version of the Sanov theorem

Mauro Mariani and Lorenzo Zambotti

Full-text: Open access


Large deviations for the local time of a process $X_i$ are investigated, where $X_i=x_i$ for $t∈[S_{i-1},S_i[$ and $(x_j)$ are i.i.d. random variables on a Polish space, S_j is the $j$-th arrival time of a renewal process depending on $(x_j)$. No moment conditions are assumed on the arrival times of the renewal process.

Article information

Electron. Commun. Probab., Volume 19 (2014), paper no. 69, 13 pp.

Accepted: 8 October 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K05: Renewal theory
Secondary: 60F10: Large deviations

Large deviations Renewal processes Sanov Theorem Heavy tails

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


Mariani, Mauro; Zambotti, Lorenzo. A renewal version of the Sanov theorem. Electron. Commun. Probab. 19 (2014), paper no. 69, 13 pp. doi:10.1214/ECP.v19-3325. https://projecteuclid.org/euclid.ecp/1465316771

Export citation


  • Asmussen, Soren. Applied probability and queues. Second edition. Applications of Mathematics (New York), 51. Stochastic Modelling and Applied Probability. Springer-Verlag, New York, 2003. xii+438 pp. ISBN: 0-387-00211-1
  • Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications. Jones and Bartlett Publishers, Boston, MA, 1993. xiv+346 pp. ISBN: 0-86720-291-2
  • Donsker, M. D.; Varadhan, S. R. S. Asymptotic evaluation of certain Markov process expectations for large time. I. II. Comm. Pure Appl. Math. 28 (1975), 1–47; ibid. 28 (1975), 279–301.
  • Kipnis, Claude; Landim, Claudio. Scaling limits of interacting particle systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 320. Springer-Verlag, Berlin, 1999. xvi+442 pp. ISBN: 3-540-64913-1
  • Lefevere, Raphael; Mariani, Mauro; Zambotti, Lorenzo. Large deviations for renewal processes. Stochastic Process. Appl. 121 (2011), no. 10, 2243–2271.
  • Lefevere, Raphael; Mariani, Mauro; Zambotti, Lorenzo. Large deviations of the current in stochastic collisional dynamics. J. Math. Phys. 52 (2011), no. 3, 033302, 22 pp.
  • Lefevere, Raphael; Mariani, Mauro; Zambotti, Lorenzo. Large deviations for a random speed particle. ALEA Lat. Am. J. Probab. Math. Stat. 9 (2012), no. 2, 739–760.
  • M. Mariani, A $\Gamma$-convergence approach to large deviations Ann. Sc. Norm. Super. Pisa Cl. Sci. (to appear).%%%
  • Lefevere R., Zambotti L., textitHot scatterers and
  • Stroock, Daniel W. Probability theory. An analytic view. Second edition. Cambridge University Press, Cambridge, 2011. xxii+527 pp. ISBN: 978-0-521-13250-3
  • Tsirelson, Boris. From uniform renewal theorem to uniform large and moderate deviations for renewal-reward processes. Electron. Commun. Probab. 18 (2013), no. 52, 13 pp.