Conference abstracts

Session A7 - Stochastic Computation

July 10, 16:00 ~ 16:25

Weak error analysis via functional Itô calculus

Felix Lindner

University of Kaiserslautern, Germany   -   lindner@mathematik.uni-kl.de

Weak errors of numerical approximations of SDEs are relatively well understood in the case where the considered functional of the solution process depends only on an evaluation of the solution at a given time $T$. In contrast, the number of available results in the literature on weak convergence rates for approximations of path-dependent functionals of SDEs is quite limited. In this talk, I present a new approach to analyzing weak approximation errors for path-dependent functionals of SDEs, based on tools from functional Ito calculus such as the functional Itô formula and functional Kolmogorov equation. It leads to a general representation formula for weak errors of the form $\mathbb{E}(f(X)-f(\tilde{X}))$, where $X$ and $\tilde{X}$ are the solution process and its approximation and the functional $f:C([0,T],\mathbb{R}^d)\to\mathbb{R}$ is assumed to be sufficiently regular. The representation formula can be used to derive explicit convergence rates, such as rate $1$ for the linearly time-interpolated explicit Euler method. Finally, I will outline how the presented approach can be extended to numerical methods for mild solutions of SPDEs.

Joint work with Mihály Kovács (Chalmers University of Technology, Sweden) and Saeed Hadjizadeh (University of Kaiserslautern, Germany).

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