- Date: 24 July. (Thu.)
- Place: West Wing, 6th floor, Colloquium Room and on the Web (zoom)
- Time: 16:50-17:50
- Speaker: Dai Taguchi (Kansai University)
- Title: Approximation of irregular functionals of SDEs
- Abstract:
Avikainen (2009) provided a sharp upper bound for the expectation of |1_{D}(X)-1_{D}(Y)|^{p} by the expectation of |X-Y|^{q}, for any one-dimensional random variables X with a bounded density function and Y, and intervales D. Then Giles and Xie (2017) give a simple proof. For multidimensional case, if both random variables X and Y have bounded densities, then this estimate is generalized by Taguchi, Tanaka and Yuasa (2022) for D with smooth boundary. In this talk, we generalize these results to the case where only one of X and Y has bounded density function and more general domain D (e.g. Lipschitz domains, convex sets). We apply our main result to numerical approximation for irregular functional of a solution to stochastic differential equations (SDEs) based on the Euler–Maruyama scheme and the multilevel Monte Carlo method. This is based on an ongoing research work with Hoang-Long Ngo (Hanoi National University of Education).
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