On nonlinear evolution equations for occupancies
type: Item
instance of: scholarly article
title: On nonlinear evolution equations for occupancies
zbMATH Open document ID: 1002.60014
DOI: 10.1023/A:1011394732405
author: V. P. Maslov
author: Alexander M. Chebotarev
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-06-16T00:00:00Z
review text: For any natural number \(N\) subspaces of the direct product of \(N\) copies of a discrete probability space \(\Omega_0\), factored with respect to the group of permutation of indices, are defined by means of arbitrary linear constraints on occupancies. The direct sum of such quotient products over \(N\in \{1,2,\dots\}\) is considered. The formula for the characteristic functional of the occupation numbers is derived. Assuming that \(\Omega_0\) is a state space of the continuous time homogeneous Markov chain, the system of nonlinear evolution equations for the mean values of the occupation numbers is obtained. The solution of the Cauchy problem for these equations is represented as a composition of a solution of a linear Markov evolution equation and a solution of the defined first-order nonlinear ordinary differential equation. Some examples are discussed in detail.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J75
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 82C10
zbMATH DE Number: 1756285
zbMATH Keywords: quotient probability spaces
zbMATH Keywords: occupancies
zbMATH Keywords: Markov evolution
zbMATH Keywords: Bose and Fermi particles
zbMATH Keywords: financial bubbles
MaRDI profile type: Publication
full work available at URL: a:1011394732405
OpenAlex ID: W52578949
description: scientific article; zbMATH DE number 1756285