By introducing a concept of dynamic process operating under multi-time scales in sciences and engineering, a mathematical model is formulated and it leads to a system of multi-time scale stochastic differential equations. The classical Picard-Lindel\"{o}f successive approximations scheme is expended to the model validation problem, namely, existence and uniqueness of solution process. Naturally, this generates to a problem of finding closed form solutions of both linear and nonlinear multi-time scale stochastic differential equations. To illustrate the scope of ideas and presented results, multi-time scale stochastic models for ecological and epidemiological processes in population dynamic are exhibited. Without loss in generality, the modeling and analysis of three time-scale fractional stochastic differential equations is followed by the development of the numerical algorithm for multi-time scale dynamic equations. The development of numerical algorithm is based on the idea if numerical integration in the context of the notion of multi-time scale integration. The multi-time scale approach is applied to explore the study of higher order stochastic differential equations (HOSDE) is presented. This study utilizes the variation of constant parameter technique to develop a method for finding closed form solution processes of classes of HOSDE. Then then probability distribution of the solution processes in the context of the second order equations is investigated.
| Identifer | oai:union.ndltd.org:USF/oai:scholarcommons.usf.edu:etd-5579 |
| Date | 01 January 2012 |
| Creators | Pedjeu, Jean-Claude |
| Publisher | Scholar Commons |
| Source Sets | University of South Flordia |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Graduate School Theses and Dissertations |
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