Doctoral Dissertations
Abstract
"We propose a new area of mathematics, namely stochastic dynamic equations, which unifies and extends the theories of stochastic differential equations and stochastic difference equations. After giving a brief introduction to the theory of dynamic equations on time scales, we construct Brownian motion on isolated time scales and prove some of its properties. Then we define stochastic integrals on isolated time scales. The main contribution of this dissertation is to give explicit solutions of linear stochastic dynamic equations on isolated time scales. We illustrate the theoretical results for dynamic stock prices and Ornstein-Uhlenbeck dynamic equations. Finally we study almost sure asymptotic stability of stochastic dynamic equations and mean-square stability for stochastic dynamic Volterra type equations"--Abstract, page iii.
Advisor(s)
Bohner, Martin, 1966-
Committee Member(s)
Akin, Elvan
Gelles, Gregory M.
Grow, David E.
Wen, Xuerong
Department(s)
Mathematics and Statistics
Degree Name
Ph. D. in Applied Mathematics
Publisher
Missouri University of Science and Technology
Publication Date
Spring 2008
Pagination
xi, 132 pages
Note about bibliography
Includes bibliographical references (pages 124-131).
Rights
© 2008 Suman Sanyal, All rights reserved.
Document Type
Dissertation - Open Access
File Type
text
Language
English
Subject Headings
Brownian motion processes -- Mathematical modelsFinance -- Mathematical modelsStochastic processes
Thesis Number
T 9395
Print OCLC #
298236220
Electronic OCLC #
244249555
Recommended Citation
Sanyal, Suman, "Stochastic dynamic equations" (2008). Doctoral Dissertations. 2276.
https://scholarsmine.mst.edu/doctoral_dissertations/2276