A notion of semi-selfsimilarity of R d -valued stochastic processes is introduced as a natural extension of the selfsimilarity. Several topics on semi-selfsimilar processes are studied: 1. The existence of the exponent of semi-selfsimilar processes. 2. Characterization for semi-selfsimilar processes as scaling limits. 3. Relationship between semi-selfsimilar processes with independent increments and semi-selfdecomposable distributions. 4. Construction of semi-selfsimilar processes with stationary increments. Semi-stable processes where all joint distributions are multivariate semi-stable are also discussed in connection with semi-selfsimilar processes.

The following forms of notation are used throughout this dissertation: 1. A lower case letter underlined, I.e., ~ indicates a column vector. 2. An upper case letter, i.e., A, indicates a matrix. Unless specifically indicated all matrices are square-symmetric. 3. A prime (') following a matrix indicates the transpose of the matrix. In particular,! ' is a row vector. 4. A subscript enclosed in parentheses and following the symbol for a variable indicates the numerical rank of the variable. For example, in an'array of k x values, x(i) has the i-th largest numerical value in the array. 5. The letter E with no other marking and preceding a function enclosed in parentheses or brackets stands for "the mathematical expectation of."

Contract AF 49(638)-213 It is shown how matrices used in error-correcting codes can be derived from Abelian group characters. Qualified requestors may obtain copies of this report from the ASTIA Document