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Freidlin Wentzell for stochastic differential inclusions

Consider the SDI $$dX^\varepsilon(t)\in b(X^\varepsilon(t))\,dt + \varepsilon \sigma(X^\varepsilon(t)) \, dB(t).$$ Is there any Freidlin-Wentzell large deviations principle for $X^\varepsilon$?
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What exactly is the relationship between Donsker-Varadhan variational formula and the Laplac...

Given a nice real valued functional $C$ on some probability space $(\Omega, \mathcal F, P_0)$ we have the following Donsker-Varadhan variational representation $$\log E_{P_0}\left[e^C\right]=\sup_{P\s …