Sharp estimates for the convergence of the density of the Euler scheme in small time

Emmanuel Gobet (Laboratoire Jean Kuntzmann Université de Grenoble)
Céline Labart (INRIA Paris Rocquencourt)

Abstract


In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.

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

Pages: 352-363

Publication Date: June 24, 2008

DOI: 10.1214/ECP.v13-1393

References

  1. Aronson D.G., 1967. Bounds for the fundamental solution of a parabolic equation. Bulletin of the American Mathematical Society, 73, 890-903. Math. Review 36 #534
  2. Bally, V., Talay, D., 1996. The law of Euler scheme for stochastic differential equations: convergence rate of the density. Monte Carlo Methods Appl., 2(2), 93-128. Math. Review 97k:60157
  3. Friedman A., 1964. Partial differential equations of parabolic type. Prentice-Hall Inc., Englewood Cliffs, N.J. Math. Review 31 #6062
  4. Guyon J., 2006. Euler schemes and tempered distributions. Stochastic Processes and their Applications, 116, 877-904. Math. Review 2007k:60217
  5. Konakov V., Mammen E., 2002. Edgeworth type expansions for Euler schemes for stochastic differential equations. Monte Carlo Methods Appl, 8(3), 271-285. Math. Review 2004e:60098
  6. Kusuoka S. Stroock D., 1984. Applications to the Malliavin calculus I. Stochastic Analysis, Proceeding of the Taniguchi International Symposium on Katata and Kyoto 1982. Kinokuniya, Tokyo, ItÙ K. Ed, 271-306. Math. Review 86k:60100a
  7. Labart C., 2007. PhD Thesis, Ecole Polytechnique, Paris. Available at http://pastel.paristech.org/3086/
  8. Nualart D., 2006. Malliavin Calculus and Related Topics (2nd Edition). Springer-Verlag, New York. Math. Review 2006j:60004
Bookmark and Share


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