Probability Theory and Related Fields

, Volume 106, Issue 1, pp 71–104 | Cite as

Large deviations for two scaled diffusions

  • Robert Liptser


We formulate large deviations principle (LDP) for diffusion pair (X ɛ ɛ )=(X t ɛ t ɛ ), where first component has a small diffusion parameter while the second is ergodic Markovian process with fast time. More exactly, the LDP is established for (X ɛ ɛ ) with ν ɛ (dt, dz) being an occupation type measure corresponding to ξ t ɛ . In some sense we obtain a combination of Freidlin–Wentzell’s and Donsker–Varadhan’s results. Our approach relies on the concept of the exponential tightness and Puhalskii’s theorem.

Mathematics Subject classification (1991): 60F10 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Robert Liptser
    • 1
  1. 1.Department of Electrical Engineering-Systems, Tel Aviv University, Tel Aviv 69978, Israel, (e-mail: IL

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