CONCERNING CERTAIN PROPERTIES AND THE LIMIT THEOREM OF A SIMPLE FUNCTION OF THE ITO RANDOM INTEGRAL,
Abstract
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 Tucker's 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 y(t) with a staircase has probability 1; (2) the sample function y(t) with a pure step function has a finite discontinuity in finite times; (3) the sample function y(t) has a bounded magnitude. The last two theorems only indicate the probability limits of the function of the increments of x(t).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 25, 1967
- Accession Number
- AD0653550
Entities
People
- Chia-kang Waung
Organizations
- National Air and Space Intelligence Center