Abstract
This chapter presents the basic relation between the linear potential theory and random walks. This fundamental connection relies on the observation that harmonic functions and martingales share a common cancellation property, expressed via mean value properties. We cover the following topics: the Laplace’s equation and harmonic functions, construction of the ball walk, values of the ball walk as harmonic functions, walk-regularity of boundary points, the exterior cone condition as sufficient for walk-regularity, relation to Perron solutions and relation to Brownian motion.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
