Developing Optimal Decision Strategies with Markovian Decision Process

The use of Markovian Decision Processes (MDPs) in creating the best possible decision strategies is examined in this research. When outcomes are partly controlled by a decision-maker and partially random, MDPs offer a mathematical framework for simulating decision-making. Finding strategies that optimize cumulative benefits over time while accounting for decision-making's immediate and long-term effects is the main goal. We go over the fundamental ideas of MDPs, such as states, actions, transitions, rewards, and the Bellman equation, which serves as the foundation for figuring out the best course of action. Practical aspects are also looked at, such as computer techniques for solving MDPs and situations in which MDPs work especially well. Decision-makers can systematically examine complicated decision situations by utilizing MDPs, which can result in well-informed and effective decision-making techniques across a variety of areas. Creating methods and algorithms for determining the best policies or decision-making processes within the context of MDPs is another goal. This entails formulating techniques to calculate ideal policies that traverse a series of states and acts in a way that maximizes long-term rewards. The study provides some information about MPs as well as specific conclusions pertaining to martingales. We show the obtained results on a general finite-dimensional filter. This work presents some findings on a general finite dimensional filter, semi-martingale decomposition, Zakai recursion, and related findings about smoothers in different contexts. After deriving the log-likelihood function, it is shown to be both increasing and convergent. Furthermore, the MLE of the parameter has been found.