Summary
In this work we study standard Euler updates for simulating stopped diffusions. We make extensive use of the fact that in many applications approximations have to be good only in the weak sense. This means that for good convergence properties only an accurate approximation of the distribution is essential whereas path wise convergence is not needed. Consequently, we sample needed random variables from their analytical distributions (or suitable approximations). As an immediate application we discuss the computation of first exit times of diffusions from a domain. We focus on one dimensional situations but illustrate extensions and applications in higher dimensional settings.
We include a series of numerical experiments confirming the conjectured accuracy of our methods (they are of weak order one).
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Buchmann, F., Petersen, W. (2006). Weak Approximation of Stopped Dffusions. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_3
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DOI: https://doi.org/10.1007/3-540-31186-6_3
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