Under a uniform convergence condition on the conditional log mgf to an essentially smooth A, the process obeys a uniform conditional local LDP, extendable to finite-dimensional and functional LDPs under extra oscillation controls.
On large deviation principles in metric spaces Siberian Math
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On large deviation principles for general random processes
Under a uniform convergence condition on the conditional log mgf to an essentially smooth A, the process obeys a uniform conditional local LDP, extendable to finite-dimensional and functional LDPs under extra oscillation controls.