28 research outputs found
Momentum-Space Approach to Asymptotic Expansion for Stochastic Filtering
This paper develops an asymptotic expansion technique in momentum space for
stochastic filtering. It is shown that Fourier transformation combined with a
polynomial-function approximation of the nonlinear terms gives a closed
recursive system of ordinary differential equations (ODEs) for the relevant
conditional distribution. Thanks to the simplicity of the ODE system, higher
order calculation can be performed easily. Furthermore, solving ODEs
sequentially with small sub-periods with updated initial conditions makes it
possible to implement a substepping method for asymptotic expansion in a
numerically efficient way. This is found to improve the performance
significantly where otherwise the approximation fails badly. The method is
expected to provide a useful tool for more realistic financial modeling with
unobserved parameters, and also for problems involving nonlinear measure-valued
processes.Comment: revised version for publication in Ann Inst Stat Mat
Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition
Hierarchical uncertainty quantification can reduce the computational cost of
stochastic circuit simulation by employing spectral methods at different
levels. This paper presents an efficient framework to simulate hierarchically
some challenging stochastic circuits/systems that include high-dimensional
subsystems. Due to the high parameter dimensionality, it is challenging to both
extract surrogate models at the low level of the design hierarchy and to handle
them in the high-level simulation. In this paper, we develop an efficient
ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the
surrogate models at the low level. In order to avoid the curse of
dimensionality, we employ tensor-train decomposition at the high level to
construct the basis functions and Gauss quadrature points. As a demonstration,
we verify our algorithm on a stochastic oscillator with four MEMS capacitors
and 184 random parameters. This challenging example is simulated efficiently by
our simulator at the cost of only 10 minutes in MATLAB on a regular personal
computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD
of Integrated Circuits and System