- Date: 23 Apr. (Thu.)
- Place: On the Web
- Time: 16:30-18:00
- Speaker: Dai Taguchi (Okayama University)
- Title: Multi-dimensional Avikainen’s estimates
- Abstract:
Avikainen provided a sharp upper bound of the expectation of |f(X)-f(Y)|^{q} by the expectation of |X-Y|^{p}, for any one-dimensional random variables X with bounded density and Y, and function of bounded variation f. In this talk, we consider multi-dimensional analogues of this estimate for any function of bounded variation in R^{d}, Orlicz–Sobolev spaces, Sobolev spaces with variable exponents or fractional Sobolev spaces.
We apply main statements to the numerical analysis on irregular functional of a solution to stochastic differential equations based on the Euler–Maruyama scheme and the multilevel Monte Carlo method, and L^{2}-time regularity of decoupled forward–backward stochastic differential equations with irregular terminal conditions.
This is joint work with Akihiro Tanaka (Osaka university) and Tomooki Yuasa (Ritsumeikan University).
We apply main statements to the numerical analysis on irregular functional of a solution to stochastic differential equations based on the Euler–Maruyama scheme and the multilevel Monte Carlo method, and L^{2}-time regularity of decoupled forward–backward stochastic differential equations with irregular terminal conditions.
This is joint work with Akihiro Tanaka (Osaka university) and Tomooki Yuasa (Ritsumeikan University).
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