We present a novel scheme for the non-adiabatic elimination of variables in stochastic processes, based on a path integral representation of the probability density and the use of an influence functional. We analyze in particular the case of multivariate Fokker-Planck equations, or equivalently a set of coupled Langevin equations driven by white noises, and discuss some examples where exact or approximate results are obtained.
AbstractThe previous paper was concerned with systems of equations over a certain family 𝓢 of quasigroups. In that work a method of elimination of an outermost variable from the system of equations was suggested and it was shown that further elimination of variables requires that the family 𝓢 of quasigroups satisfy the generalized distributive law (GDL). In this paper we describe families 𝓢 that satisfy GDL. The results are applied to construct classes of easily solvable systems of equations.
Elimination of Variables in Linear Solvable Polynomial Algebras and ∂-Holonomicity
