RANDOM WALKS WITH SPECIFIED FREQUENCIES OF OCCUPIED STATES

摘要

The class of all one step random walks in which transitions with the same state are permitted and which have a specified long term frequency of occupied states is identified. A correspondence is established between the points of a certain polytope and the transition matri¬ces for such random walks. Explicit formulae are given for a number of transition matrices with special characteristics and as a result necessary and sufficient conditions for there to be a classical one step random walk solution are obtained. Two procedures for generating transition matrices are proposed. Some comments are offered on selecting a 'good' transition matrix from among the many acceptable ones.