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Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu
Multi-Time Scales Stochastic Dynamic Processes: Modeling, Methods, Algorithms, Analysis, And Applications, Jean-Claude Pedjeu
USF Tampa Graduate Theses and Dissertations
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, …