An exposition on the theory of martingale

• Main Authors: Buendia, Anna Celeste, Jamisal, Grischelle M.
• Format: text
• Language: English
• Published: Animo Repository 1992
• Subjects: Martingales (Mathematics)
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/15968
• Institution: De La Salle University

This study provides a detailed discussion of the Martingale theory and its properties. To elaborate definitions and properties, conditional expectation is the primary theorem used in this paper.Several examples of martingale properties are presented and step by step outline of proofs for each remark is discussed. The relationships among martingale, submartingale and supermartingale are taken into account.The results of this study reveal that martingales have broad scope and diverse domains of uses in general probability theory and analysis.It is recommended that researchers pursue further studies on the other properties of martingales and emphasis be given extensively on the application of submartingales and super martingales.Further studies may be conducted on the examples of application of stochastic processes, Optional Sampling Theorem and Martingale Convergence Theorem are likewise recommended to researchers.