@Article{CiCP-10-1241,
author = {Guo-Kang Er and Vai Pan Iu},
title = {The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1241--1256},
abstract = {<p style="text-align: justify;">The probabilistic solutions of the nonlinear stochastic dynamic (NSD) systems
with polynomial type of nonlinearity are investigated with the subspace-EPC
method. The space of the state variables of large-scale nonlinear stochastic dynamic
system excited by white noises is separated into two subspaces. Both sides of the
Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system is then
integrated over one of the subspaces. The FPK equation for the joint probability density
function of the state variables in another subspace is formulated. Therefore, the
FPK equation in low dimensions is obtained from the original FPK equation in high
dimensions and it makes the problem of obtaining the probabilistic solutions of large-scale
NSD systems solvable with the exponential polynomial closure method. Examples
about the NSD systems with polynomial type of nonlinearity are given to show
the effectiveness of the subspace-EPC method in these cases.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.140710.210111a},
url = {http://global-sci.org/intro/article_detail/cicp/7482.html}
}