Introduction to Markov Processes
We introduce the concept of stochastic and Markov processes and the Chapman-Kolmogorov equations that define the latter. We show how Markov processes can be described in terms of the Markov propagator density function and the related propagator moment functions. We introduce the Kramers-Moyal equations and use them to discuss the evolution of the moments. We introduce two simple example processes that illustrate how Markov processes can be defined and characterized in practical terms. Finally, we introduce homogeneous Markov processes and show how the apparatus developed so far simplifies for this class. This module does not discuss more specific Markov processes--continuous, jump, birth-death, etc.
Chapman-Kolmogorov Equations, Evolution of the Moments, Homogeneous Markov Processes, Kramers-Moyal Equations, Markov Processes, Markov Propagator Density Function, Markov Propagator Moment Function, Stochastic Processes
Dr Zdzislaw (Gustav) Meglicki, Jr