Stochastic Processes

A stochastic process is a mathematical object that represents a collection of random variables indexed by time or space. These processes are used to model systems that evolve over time in a probabilistic manner, capturing the inherent uncertainty in their behavior. Key characteristics include state space, transition probabilities, and time parameterization, which can be discrete or continuous. Common use cases include financial modeling, queuing theory, and various applications in machine learning and artificial intelligence, where they help in predicting future states based on past events. Understanding stochastic processes is essential for grasping concepts in statistics, data analysis, and probabilistic modeling.