Publication Cover
Sequential Analysis
Design Methods and Applications
Volume 42, 2023 - Issue 2
42
Views
0
CrossRef citations to date
0
Altmetric
Articles

One-sided maximal inequalities for a randomly stopped Bessel process

Pages 182-188 | Received 28 Nov 2022, Accepted 09 Mar 2023, Published online: 23 May 2023

REFERENCES

  • Abundo, M. 2017. “The Mean of the Running Maximum of an Integrated Gauss-Markov Process and the Connection with Its First-Passage Time.” Stochastic Analysis and Applications 35 (3):499–510. doi:10.1080/07362994.2016.1273784
  • Burkholder, D. L. 1977. “Exit Times of Brownian Motion, Harmonic Majorization, and Hardy Spaces.” Advances in Mathematics 26 (2):182–205. doi:10.1016/0001-8708(77)90029-9
  • Cherny, A. S. 2000. “On the Strong and Weak Solutions of Stochastic Differential Equations Governing Bessel Processes.” Stochastics and Stochastics Reports 70 (3-4):213–9. doi:10.1080/17442500008834252
  • DeBlassie, R. Dante. 1987. “Stopping Times of Bessel Processes.” The Annals of Probability 15 (3):1044–51. doi:10.1214/aop/1176992079
  • Dubins, L. E., L. A. Shepp, and A. N. Shiryaev. 1994. “Optimal Stopping Rules and Maximal Inequalities for Bessel Processes.” Theory of Probability & Its Applications 38 (2):226–61. doi:10.1137/1138024
  • Graversen, S. E., and G. Peskir. 1998. “Maximal Inequalities for Bessel Processes.” Journal of Inequalities and Applications 2:621735. doi:10.1155/S102558349800006X
  • Lenglart, E. 1977. “Relation de Domination Entre Deux Processus.” Annales de l'Institut Henri Poincaré 13:171–9.
  • Makasu, C. 2023. “On the Exact Constants in One-Sided Maximal Inequalities for Bessel Processes.” Sequential Analysis 42 (1):35–42. doi:10.1080/07474946.2022.2150778
  • Masoliver, J. 2014. “Extreme Values and the Level-Crossing Problem: An Application to the Feller Process.” Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 89 (4):042106. doi:10.1103/PhysRevE.89.042106
  • Peskir, G. 1998. “Optimal Stopping of the Maximum Process: The Maximality Principle.” The Annals of Probability 26 (4):1614–40. doi:10.1214/aop/1022855875
  • Revuz, D., and M. Yor. 1991. Continuous Martingales and Brownian Motion. New York: Springer-Verlag.
  • Rosenkrantz, W. A., and S. Sawyer. 1977. “Lp Estimates for Stopping Times of Bessel Processes.” Zeitschrift für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 41 (2):145–51. doi:10.1007/BF00538418
  • Schachermayer, W., and F. Stebegg. 2018. “The Sharp Constant for the Burkholder-Davis-Gundy Inequality and Non-Smooth Pasting.” Bernoulli 24 (4A):2499–530. doi:10.3150/17-BEJ935
  • Shiga, T., and S. Watanabe. 1973. “Bessel Diffusions as a One-Parameter Family of Diffusion Processes.” Zeitschrift für Wahrscheinlichkeitstheorie Und Verwandte Gebiete 27 (1):37–46. doi:10.1007/BF00736006
  • Yan, L., and B. Zhu. 2004. “A Ratio Inequality for Bessel Processes.” Statistics & Probability Letters 66 (1):35–44. doi:10.1016/j.spl.2003.10.003
  • Yasue, A. 2004. “Bessel-like Processes and SDE.” Journal of Mathematics of Kyoto University 44:799–809.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.