Abstract
One investigates the representation of the probabilities of nonexit of a Brownian motion from a curvilinear strip in the form of an expansion with respect to a system of eigenfunctions. It is shown that the coefficients of this series satisfy a Volterra integral equation in l2. For thin strips, with bounded first derivatives of the boundaries, the successive iterations of the equation determine a complete asymptotic expansion of the nonexit probabilities.
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