Large deviations for two scaled diffusions

Summary. We formulate large deviations principle (LDP) for diffusion pair (X ^ɛ ,ξ ^ɛ )=(X _t ^ɛ ,ξ _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 ,ν ^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. Received: 29 June 1995/In revised form: 14 February 1996