Bernoulli

  • Bernoulli
  • Volume 11, Number 2 (2005), 247-262.

Large-noise asymptotics for one-dimensional diffusions

Szymon Peszat and Francesco Russo

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Abstract

We establish a law of large numbers and a central limit theorem for a class of additive functionals related to the solution of a one-dimensional stochastic differential equation perturbed by a large noise.

Article information

Source
Bernoulli, Volume 11, Number 2 (2005), 247-262.

Dates
First available in Project Euclid: 17 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1116340293

Digital Object Identifier
doi:10.3150/bj/1116340293

Mathematical Reviews number (MathSciNet)
MR2132725

Zentralblatt MATH identifier
1072.60014

Keywords
additive functional central limit theorem large noise law of large numbers stochastic differential equations

Citation

Peszat, Szymon; Russo, Francesco. Large-noise asymptotics for one-dimensional diffusions. Bernoulli 11 (2005), no. 2, 247--262. doi:10.3150/bj/1116340293. https://projecteuclid.org/euclid.bj/1116340293


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References

  • [1] Flandoli, F. and Russo, F. (2002) Generalized calculus and SDEs with non-regular drift. Stochastics Stochastics Rep., 72, 11-54.
  • [2] Le Gall, J.F. (1983) Applications du temps local aux équations différentielles stochastiques unidimensionnelles. In J. Azéma and M. Yor (eds), Séminaire de Probabilités XVII, Lecture Notes in Math. 986, pp. 15-31. Berlin: Springer-Verlag.
  • [3] Nakao, S. (1972) On the pathwise uniqueness of one-dimensional stochastic differential equations. Osaka J. Math., 9, 513-518.
  • [4] Perkins, E. (1982) Local time and pathwise uniqueness for stochastic differential equations. In J. Azéma and M. Yor (eds), Séminaire de Probabilités XVI, Lecture Notes in Math. 920, pp. 201- 208. Berlin: Springer-Verlag.
  • [5] Remillard, B. (2000) Large deviations for occupation time integrals of Brownian motion. In L.G. Gorostiza and G. Ivanoff (eds), Stochastic Models, A Volume in Honor of Donald A. Dawson, pp. 375-398. Providence, RI: American Mathematical Society.
  • [6] Revuz, D. and Yor, M. (1999) Continuous Martingales and Brownian Motion. Berlin: Springer-Verlag.
  • [7] Russo, F. and Oberguggenberger, M. (1999) White noise driven stochastic partial differential equations: triviality and non-triviality. In M. Grosser, G. Hö rmann, M. Kunzinger and M. Oberguggenberger (eds), Nonlinear Theory of Generalized Functions, pp. 315-333, Research Notes in Math. Series. Boca Raton, FL.: Chapman & Hall/CRC.
  • [8] Takeda, M. (1998) Asymptotic properties of generalized Feynman-Kac functionals. Potential Anal., 5, 261-291.
  • [9] Takeda, M. (2003) Large deviation principle for additive functionals of Brownian motion corresponding to Kato measures. Potential Anal., 19, 51-67.
  • [10] Yamada, T. (1986) On some limit theorems for occupation times of one dimensional Brownian motion and its continuous additive functionals locally of zero energy. J. Math. Kyoto Univ., 26, 309-322.
  • [11] Yamada, T. (1996) Principal values of Brownian local times and their related topics. In N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita (eds), Ito ´s Stochastic Calculus and Probability Theory, pp. 413-422. Tokyo: Springer-Verlag.