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Diffusion approximation for slow motion in fully coupled averaging
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  • Published: 03 March 2004

Diffusion approximation for slow motion in fully coupled averaging

  • Victor Bakhtin1 &
  • Yuri Kifer2 

Probability Theory and Related Fields volume 129, pages 157–181 (2004)Cite this article

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  • 33 Citations

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Abstract.

In systems which combine fast and slow motions it is usually impossible to study directly corresponding two scale equations and the averaging principle suggests to approximate the slow motion by averaging in fast variables. We consider the averaging setup when both fast and slow motions are diffusion processes depending on each other (fully coupled) and show that there exists a diffusion process which approximates the slow motion in the $L^2$ sense much better than the averaged motion prescribed by the averaging principle.

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Author information

Authors and Affiliations

  1. Department of Physics, Belarusian State University, Fr. Scoriny 4, Minsk, 220050

    Victor Bakhtin

  2. Institute of Mathematics, The Hebrew University, Jerusalem, 91904, Israel

    Yuri Kifer

Authors
  1. Victor Bakhtin
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  2. Yuri Kifer
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Corresponding author

Correspondence to Victor Bakhtin.

Additional information

The authors are partially supported by INTAS, project No. 99-00559 and by US-Israel BSF, respectively. Part of the work was done during the visit of the 1st author to the Hebrew University.

Mathematics Subject Classification (2000): Primary 34C29; Secondary 60F15, 58J65

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Cite this article

Bakhtin, V., Kifer, Y. Diffusion approximation for slow motion in fully coupled averaging. Probab. Theory Relat. Fields 129, 157–181 (2004). https://doi.org/10.1007/s00440-003-0326-7

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  • Received: 10 May 2003

  • Revised: 24 October 2003

  • Published: 03 March 2004

  • Issue Date: June 2004

  • DOI: https://doi.org/10.1007/s00440-003-0326-7

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Keywords

  • Averaging
  • Diffusion
  • Limit theorems
  • Stochastic differential equations
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