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Ergodic Theorems for a Certain Class of Markoff Processes


Kennedy, Maurice (1954) Ergodic Theorems for a Certain Class of Markoff Processes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z1NN-R156.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Mathematics and Physics)
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Karlin, Samuel
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1954
Record Number:CaltechETD:etd-01072004-100602
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:46
Deposited By: Imported from ETD-db
Deposited On:08 Jan 2004
Last Modified:09 Jun 2023 00:00

Thesis Files

PDF (Kennedy_m_1954.pdf) - Final Version
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