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Asymptotic expansions for SDE’s with small multiplicative noise

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  • Albeverio, Sergio
  • Smii, Boubaker

Abstract

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Suggested Citation

  • Albeverio, Sergio & Smii, Boubaker, 2015. "Asymptotic expansions for SDE’s with small multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1009-1031.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:3:p:1009-1031
    DOI: 10.1016/j.spa.2014.09.009
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    References listed on IDEAS

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    1. Victoria Steblovskaya & Sergio Albeverio, 2002. "A model of financial market with several interacting assets. Complete market case," Finance and Stochastics, Springer, vol. 6(3), pages 383-396.
    2. Duan, Jinqiao & Yan, Jia-an, 2008. "General matrix-valued inhomogeneous linear stochastic differential equations and applications," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2361-2365, October.
    3. Masayuki Uchida & Nakahiro Yoshida, 2004. "Asymptotic Expansion for Small Diffusions Applied to Option Pricing," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 189-223, October.
    4. Albeverio, Sergio & Mastrogiacomo, Elisa & Smii, Boubaker, 2013. "Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2084-2109.
    5. Albeverio, S. & Mandrekar, V. & Rüdiger, B., 2009. "Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 835-863, March.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Liang, Song, 2016. "Stochastic Newton equation in strong potential limit," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 2913-2955.

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