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Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales

Author

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  • Bhattacharya, Rabi
  • Denker, Manfred
  • Goswami, Alok

Abstract

The present article analyses the large-time behavior of a class of time-homogeneous diffusion processes whose spatially periodic dynamics, although time independent, involve a large spatial parameter 'a'. This leads to phase changes in the behavior of the process as time increases through different time zones. At least four different temporal regimes can be identified: an initial non-Gaussian phase for times which are not large followed by a first Gaussian phase, which breaks down over a subsequent region of time, and a final Gaussian phase different from the earlier phases. The first Gaussian phase occurs for times 1 > a2 log a; or, it may take an enormous amount of time t >> exp{ca} for some c>0. An estimation of the speed of convergence to equilibrium of diffusions on a circle of circumference 'a' is provided for the above analysis.

Suggested Citation

  • Bhattacharya, Rabi & Denker, Manfred & Goswami, Alok, 1999. "Speed of convergence to equilibrium and to normality for diffusions with multiple periodic scales," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 55-86, March.
    • Handle: RePEc:eee:spapps:v:80:y:1999:i:1:p:55-86
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    Cited by:

    1. Pai, Hui-Ming & Hwang, Chii-Ruey, 2013. "Accelerating Brownian motion on N-torus," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1443-1447.

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