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Recurrence and ergodicity of diffusions

Author

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  • Bhattacharya, R. N.
  • Ramasubramanian, S.

Abstract

This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a limiting stationary homogenous diffusion. A functional central limit theorem is proved for the class of positive recurrent homogeneous diffusions. Upper and lower functions for positive recurrent nonhomogeneous diffusions are also studied.

Suggested Citation

  • Bhattacharya, R. N. & Ramasubramanian, S., 1982. "Recurrence and ergodicity of diffusions," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 95-122, March.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:1:p:95-122
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    Citations

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    Cited by:

    1. Ben Hambly & Nikolaos Kolliopoulos, 2020. "Fast mean-reversion asymptotics for large portfolios of stochastic volatility models," Finance and Stochastics, Springer, vol. 24(3), pages 757-794, July.
    2. Takashi Kamihigashi & John Stachurski, 2014. "Stability Analysis for Random Dynamical Systems in Economics," Discussion Paper Series DP2014-35, Research Institute for Economics & Business Administration, Kobe University.
    3. Ben Hambly & Nikolaos Kolliopoulos, 2018. "Fast mean-reversion asymptotics for large portfolios of stochastic volatility models," Papers 1811.08808, arXiv.org, revised Feb 2020.
    4. Basak, Gopal K. & Hu, Inchi & Wei, Ching-Zong, 1997. "Weak convergence of recursions," Stochastic Processes and their Applications, Elsevier, vol. 68(1), pages 65-82, May.

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