FOUNDATION OF STOCHASTIC MODELING AND APPLICATIONS
Abstract:
This thesis provides a comprehensive examination of the fundamental concepts in stochastic modeling, namely stopping times, martingales, and Brownian motion. The research begins with a meticulous investigation of discrete stopping times and their inherent properties. Through a systematic exploration, the theory of martingales is then reviewed, with a particular focus on their practical application in addressing the problem of “extinction of populations.” Building upon this foundation, the study delves into the realm of stopping times in the continuous case, expanding upon the earlier discrete analysis. Finally, the thesis extensively explores the concepts of Brownian motion and the Wiener integral, elucidating their essential characteristics and significance within stochastic modeling. By elucidating these key concepts, this research contributes to the understanding and application of stochastic modeling techniques in various fields of study.
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