Ergodic Theorems for a Certain Class of Markoff Processes

Citation

Kennedy, Maurice (1954) Ergodic Theorems for a Certain Class of Markoff Processes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z1NN-R156. https://resolver.caltech.edu/CaltechETD:etd-01072004-100602

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. A system, whose state may be described by a point t in a bounded set in Euclidean space, is considered. At every unit interval of time, attractions [...] towards certain points [...] are applied with probabilities [...], where t is the state of the system. Given the initial probability distribution [...] for the state of the system, the problem is to obtain limiting theorems for the distribution at the nth unit of time as [...]. Subject to certain conditions on [...] and [...] such convergence theorems are obtained. Some particular properties for the case, where the attractions are toward the vertices of a simplex, are discussed. Finally the one-dimensional learning model is considered.

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