"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.
Bohner, Martin, 1966-
Gelles, Gregory M.
Grow, David E.
Mathematics and Statistics
Ph. D. in Applied Mathematics
Missouri University of Science and Technology
xi, 132 pages
© 2008 Suman Sanyal, All rights reserved.
Dissertation - Open Access
Library of Congress Subject Headings
Brownian motion processes -- Mathematical models
Finance -- Mathematical models
Print OCLC #
Electronic OCLC #
Link to Catalog Record
Sanyal, Suman, "Stochastic dynamic equations" (2008). Doctoral Dissertations. 2276.