Wednesday, November 15, 2023 - 13:30 in V2-210/216
Adaptive approximation of stochastic processes
A talk in the BI.discrete Workshop series by
Michael Feischl from Wien
| Abstract: |
There are many stochastic processes which are known to be arbitrarily hard to approximate when using uniform timesteps.
This can even happen if the coefficients (drift and diffusion) of the governing stochastic differential equation are smooth. Practically more relevant is for
example the Cox-Ingersoll-Ross process, which has a square root singularity in the diffusion term. It is known that uniform approximations of the process converge
with arbitrarily small algebraic rate. We demonstrate numerically, that adaptive mesh refinement in time can overcome this barrier and deliver the expected convergence rates
of $1/2$. This is particularly interesting since multi-level approximations require exactly this rate to offer a significant performance gain.
Within the CRC this talk is associated to the project(s): A7, B3, B7 |
Back
