Markov Models

Markov models are mathematical frameworks used to model systems that transition from one state to another, where the probability of each state depends only on the previous state. They are characterized by their memoryless property, meaning that the future state is independent of past states given the present state. Commonly used in various fields, including statistics, finance, and machine learning, Markov models are particularly useful for modeling sequential data and time series. Applications include speech recognition, natural language processing, and predictive text generation, where the next state or output is determined based on the current state. Variants such as Hidden Markov Models (HMMs) extend the basic concept by incorporating hidden states to better capture the complexity of real-world phenomena.