On Markov evolution equations in quotient probability spaces (Q2702432)

Recently, factorization of probability measures on direct products of probability spaces are applied in mathematical physics [see \textit{V. P. Maslov}, Math. Notes 64, No. 3, 406-410 (1998); translation from Mat. Zametki 64, No. 3, 470-473 (1998) and \textit{A. M. Chebotarev}, ibid. 65, No. 5, 627-637 (1999) resp. ibid. 65, No. 5, 746-759 (1999; Zbl 0959.60013)] revealing simple facts which were missed both in statistical physics and in classical probability theory. The application of this method gives the chance to use noncombinatorial numerical and asymptotical estimates for probabilities of events satisfying some superselection rules; simplifies the computation of mathematical expectation values; enables the inclusion of restrictions on the occupation of states into the corresponding system of stochastic differential equations describing the stochastic evolution of a system of identical particles.NEWLINENEWLINENEWLINEThe latter is used to describe the Markovian evolution of the mean values of occupation numbers for a system of indistinguishable particles which satisfy arbitrary superselection rules. The solution of the nonlinear Cauchy problem for this equation is reduced to the solution of a linear Cauchy problem for the Kolmogorov-Feller equation coupled to the solution of a nonlinear ordinary differential equation.NEWLINENEWLINEFor the entire collection see [Zbl 0953.00048].