@bullet Muhammad Karvllil Habib. Sampling Representations and Approximations for Certain Functions and Stochastic Processes. (under the Direction of Stamatis Cambanis.)

Zakai's Class of Bandlimited Functions and Processes: Its Characterization and Properties ** Zakai I S Class of Ba1wlittlited Functions and Processes: Itsci1aracterization and Properties **

* Elias Masry Department of Applied Physics & Information Sciences University of California, San Diego La Jolla, CA 92037 This paper characterizes Zakai's class [3] of bandlimited functions and processes in terms of conventionally band1imited functions and processes. This characterization was first conjectured by Zakai and is used here to derive sharper sampling representations and to study fur...

Ph . D . dissertation under the direction of Stamatis

Consider a stochastic process {x(t), t€T} of random elements of a Hilbert space H, whose index set is a locally compact Hausdorff space. The results obtained in this work fall into two broad categories, first the study of weakly stationary processes and their representations, and secondly the study of the sample path properties of not necessarily . stationary processes. In each case, we choose ...

The Equivalence or Sihgularity of Stochastic Processes

On the representation of weakly continuous stochastic processes

• A novel approach to obtaining series representations in the stochastic mean for weakly, and therefore mean square, continuous stochastic processes 1s presented. Two distinct orthogonal series representations are derived for the entire class of weakly continuous stochastic processes on any Lebesgue set of the real line, and a constructive procedure to obtain them explicitly is given. They incl...

On the Theory of Elliptically Contoured Distributions

The theory of elliptically contoured distributions is presented in an unrestricted setting (without reference to moment restrictions or assumptions of absolute continuity). These distributions are defined parametrically through their characteristic functions, and then studied primarily through the use of stochastic representations which naturally follow from the seminal work of Schoenberg on sp...