A Markov process is a type of stochastic process where the future state of a system depends only on the current state, and not on any previous states. It is based on the principle of memorylessness, meaning that the past history of the system is not relevant to predicting its future behavior.
A traditional stochastic process takes into account the entire history of a system to predict its future behavior, whereas a Markov process only considers the current state. This makes Markov processes simpler and more efficient to model and analyze, especially for complex systems.
Diffusion refers to the random movement of particles or molecules in a system. In the context of Markov processes, diffusion is a type of stochastic process where the state of a system changes due to the random movement of its particles.
Markov processes have a wide range of applications in various fields, such as finance, biology, and physics. Some examples include modeling stock prices, predicting weather patterns, analyzing protein folding, and simulating traffic flow.
One highly recommended textbook is "Stochastic Processes and Diffusion: Theory and Applications" by Paul L. Berglund and Edward Allen Scheinerman. It provides a comprehensive introduction to Markov processes and diffusion, with clear explanations and examples, making it suitable for both students and researchers.