This book delves into the comprehensive construction of the It� theory concerning stochastic integration and its pivotal role, particularly within the framework of stochastic differential equations. The book meticulously examines the distinctive properties of this integral, along with their respective extensions of the It� formula, elucidating their significance in various theoretical and practical contexts. Furthermore, the integration theories are seamlessly integrated into the realm of stochastic differential equations, paving the way for examining complex phenomena such as epidemic models, and ecological models. In this context, the book proposes some original theorems to address pertinent issues about its implications within the framework of stochastic differential equations. Through rigorous construction analysis, this book contributes to the advancement of stochastic calculus theory, offering insights into its application in dynamical population modeling.

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