Doctoral Dissertations

Suman Sanyal

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 models
Finance -- Mathematical models
Stochastic processes

Thesis Number

T 9395

Print OCLC #

298236220

Electronic OCLC #

244249555

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