Abstract
In this chapter, we study some of the basic properties of Markov stochastic processes, and in particular, the properties of diffusion processes. In Sect. 2.1, we present various examples of Markov processes in discrete and continuous time. In Sect. 2.2, we give the precise definition of a Markov process and we derive the fundamental equation in the theory of Markov processes, the Chapman–Kolmogorov equation. In Sect. 2.3, we introduce the concept of the generator of a Markov process. In Sect. 2.4, we study ergodic Markov processes. In Sect. 2.5, we introduce diffusion processes, and we derive the forward and backward Kolmogorov equations. Discussion and bibliographical remarks are presented in Sect. 2.6, and exercises can be found in Sect. 2.7.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.