TY - JOUR
T1 - The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems
AU - Guo-Kang Er & Vai Pan Iu
JO - Communications in Computational Physics
VL - 5
SP - 1241
EP - 1256
PY - 2011
DA - 2011/10
SN - 10
DO - http://doi.org/10.4208/cicp.140710.210111a
UR - https://global-sci.org/intro/article_detail/cicp/7482.html
KW - 
AB - <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>