Non-Markovian process driven by quadratic noise: Kramers-Moyal expansion and Fokker-Planck modeling
Physical Review E, 1995•APS
A linear non-Markovian process driven by additive exponentially correlated Gaussian
quadratic noise is considered. An exact master equation for a probability distribution of the
process is presented. A Kramers-Moyal-type expansion of the master equation is studied.
Some limiting cases of the expansion are investigated. It is demonstrated that any finite
truncation of the expansion fails. An alternative and correct Fokker-Planck modeling is
constructed.
quadratic noise is considered. An exact master equation for a probability distribution of the
process is presented. A Kramers-Moyal-type expansion of the master equation is studied.
Some limiting cases of the expansion are investigated. It is demonstrated that any finite
truncation of the expansion fails. An alternative and correct Fokker-Planck modeling is
constructed.
Abstract
A linear non-Markovian process driven by additive exponentially correlated Gaussian quadratic noise is considered. An exact master equation for a probability distribution of the process is presented. A Kramers-Moyal-type expansion of the master equation is studied. Some limiting cases of the expansion are investigated. It is demonstrated that any finite truncation of the expansion fails. An alternative and correct Fokker-Planck modeling is constructed.
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