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Inverse method of images. (English) Zbl 1001.60084

Summary: We consider the problem of approximating the density of the time at which a Brownian path first crosses a curved boundary in cases where the exact density is not known or is difficult to compute. Approximation methods which involve the use of images will be proposed. These methods can be used not only for one-sided boundaries but also for the case of two-sided boundaries, and not only for concave boundaries but also for convex boundaries. The square root boundary and parabolic boundary provide examples for numerical comparisons of the approximation methods.

MSC:

60J65 Brownian motion
60J50 Boundary theory for Markov processes
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