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CONCERNING CERTAIN PROPERTIES AND THE LIMIT THEOREM OF A SIMPLE FUNCTION OF THE ITO RANDOM INTEGRAL,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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This paper discusses the properties and limit theorems of a sample function of the Ito stochastic integral. Most of the results in this paper can be regarded as a generalization of Cogburn and Tuckers limit theorem for a function of increments of a decomposable process. The paper begins with a derivation of certain properties of the sample function of the stochastic process defined by an Ito stochastic integral. Then the author uses the derived result in an investigation of analogous limit theorems. Five theorems are stated and proved in the paper. The first three theorems show that 1 the sample function yt with a staircase has probability 1 2 the sample function yt with a pure step function has a finite discontinuity in finite times 3 the sample function yt has a bounded magnitude. The last two theorems only indicate the probability limits of the function of the increments of xt.
APPROVED FOR PUBLIC RELEASE