Enhancing Reliability and Accuracy in Stochastic Growth Modeling: Method of Three Selected Points Approach

Growth models play a pivotal role in diverse fields, such as population dynamics, epidemiology, finance, and ecological systems. Traditionally, deterministic growth models have been extensively employed to capture various aspects of growth phenomena. However, in real-world scenarios, stochasticity is inherent in the data, challenging the suitability of deterministic models. Consequently, there is a growing interest in developing stochastic growth models capable of accommodating inherent uncertainties. This study addresses three fundamental questions within the context of stochastic growth modeling. Firstly, it investigates the continued reliability of the  Method of Three Selected Points (MTSP) for estimating parameters in stochastic differential equations (SDEs), given the increasing popularity of stochastic models over deterministic ones. Secondly, it explores the required form of SDEs that maximizes the success and reliability of the MTSP approach. Lastly, it conducts a comparative analysis of the MTSP method against commonly employed techniques in the literature.