
Accession Number : AD0694132
Title : ON MARKOVIAN LATTICES,
Corporate Author : HAWAII UNIV HONOLULU INFORMATION SCIENCES PROGRAM
Personal Author(s) : Gaarder,N. Thomas
Report Date : 28 JUL 1969
Pagination or Media Count : 48
Abstract : In many information processing problems one is confronted with modeling a random quantity that depends upon two, or more, parameters. A natural model for such a quantity is a random function of multidimensional argument; i.e., a random field. In this paper we consider random fields that are defined on only a discrete set of points; the points from a rectangular lattice in an ndimensional space. The Markovian property of processes is extended to include such random fields. The extension is nontrivial since the concept of a preferential direction is lost in the transition to a multidimensional argument. In addition, Levy's definition of a Markov random field on all of nspace is not easily extended to a field defined on a lattice. Particular emphasis is given to homogeneous random lattices; a homogenous lattice is one with probabilities that are invariant to all coordinate translations. Discrete, homogeneous, Markov lattices are practically determined by n commutative transition matrices  one for each principle coordinate of the space  and an 'initial condition'. Another useful property of random fields is isotropy, or invariance to all coordinate rotations, as well as to all coordinate translations. It is shown that there are no isotropic, Markov lattices other than the trivial 'white' one. (Author)
Descriptors : (*DATA PROCESSING, INFORMATION THEORY), (*STOCHASTIC PROCESSES, MATHEMATICAL MODELS), PATTERN RECOGNITION, MEASURE THEORY, PROBABILITY, SET THEORY, THEOREMS
Subject Categories : Operations Research
Cybernetics
Distribution Statement : APPROVED FOR PUBLIC RELEASE