We develop variational approximations to the survival probability for chemical reactions that are coupled to a Markovian stochastic environment. These approximations provide upper and lower bounds and are able to capture the correct asymptotic behavior for both a slowly fluctuating environment and a rapidly relaxing environment. Intermittency, as observed in single molecule experiments, can also be computed using the same approximations. We highlight the relationship of these approximations to previous approaches and compare variational results to exactly solvable examples.
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