Abstract
We outline our general scheme of proof of lower bounds in the simple case of p-stable processes by combining the fact that they are conditionally Gaussian with our results on Gaussian processes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
If you have already glanced through the rest of the book, you should be aware that a basic reason the special case of p-stable processes is simple is that these processes are conditionally Gaussian. Many more processes of interest (such as infinitely divisible processes) are not conditionally Gaussian, but are conditionally Bernoulli.
- 2.
It is explained in the proof of Theorem 11.7.1 how to cover the case where T is countable.
- 3.
We know now how to give much simpler proofs than those of [132].
References
Ledoux, M., Talagrand, M.: Probability in Banach spaces: isoperimetry and processes. In: Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 23, xii+480 pp. Springer, Berlin (1991). ISBN: 3-540-52013-9
Talagrand, M.: Upper and Lower Bounds for Stochastic Processes, 1st edn. Springer, Berlin (2014)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Talagrand, M. (2021). Warming Up with p-Stable Processes. In: Upper and Lower Bounds for Stochastic Processes. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-030-82595-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-82595-9_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-82594-2
Online ISBN: 978-3-030-82595-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)