Abstract
The results and discussions of Chapter 11 do not readily extend to cover a multiparameter process such as the Brownian sheet, since the latter is not a multiparameter Markov process according to the definitions of Chapter 11. In this regard, see Exercise 1.1.3, Chapter 11. In the first section of this chapter we extend and refine the arguments of Chapter 11 to estimate intersection probabilities for the range of the Brownian sheet. As in the development of Chapter 11, these estimates yield geometric information about the range of the Brownian sheet by way of Hausdorff dimension calculations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Khoshnevisan, D. (2002). The Brownian Sheet and Potential Theory. In: Multiparameter Processes. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/0-387-21631-6_12
Download citation
DOI: https://doi.org/10.1007/0-387-21631-6_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3009-5
Online ISBN: 978-0-387-21631-7
eBook Packages: Springer Book Archive