Random Walks Associated with Non-Divergence Form Elliptic Equations

Joseph G. Conlon and Renming Song
Additional contact information
Joseph G. Conlon: University of Michigan
Renming Song: University of Illinois

Journal of Theoretical Probability, 2000, vol. 13, issue 2, 427-489

Abstract: Abstract This paper is concerned with the study of the diffusion process associated with a nondivergence form elliptic operator in d dimensions, d≥2. The authors introduce a new technique for studying the diffusion, based on the observation that the probability of escape from a d−1 dimensional hyperplane can be explicitly calculated. They use the method to estimate the probability of escape from d−1 dimensional manifolds which are C 1, α , and also d−1 dimensional Lipschitz manifolds. To implement their method the authors study various random walks induced by the diffusion process, and compare them to the corresponding walks induced by Brownian motion.

Keywords: diffusion process; elliptic operator; Lipschitz manifolds; random walks (search for similar items in EconPapers)
Date: 2000
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1007893424255 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:13:y:2000:i:2:d:10.1023_a:1007893424255

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1007893424255

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().