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Small-noise approximations to the solution of the Smoluchowski equation.

We explore the connection between the two perturbation methods that have been suggested for solving Smoluchowski-like equations with weak noise. A slight modification of the first of these methods (the size expansion of van Kampen) makes it identical to the second (the method of running coordinates). We point out that a number of modifications to both methods are possible and should be explored. We illustrate the advantages of both of these methods as applied to three solvable examples.