Bridges with Random Length: Gamma Case

Author:

Erraoui Mohamed,Hilbert AstridORCID,Louriki Mohammed

Abstract

Abstract In this paper, we generalize the concept of gamma bridge in the sense that the length will be random, that is, the time to reach the given level is random. The main objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. We show that the gamma bridge with random length is a pure jump process and that its jumping times are countable and dense in the random interval bounded by 0 and the random length. Moreover, we prove that this process is a Markov process with respect to its completed natural filtration as well as with respect to the usual augmentation of this filtration, which leads us to conclude that its completed natural filtration is right continuous. Finally, we give its canonical decomposition with respect to the usual augmentation of its natural filtration.

Funder

Erasmus plus Credit Mobility

Publisher

Springer Science and Business Media LLC

Subject

Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability

Reference25 articles.

1. Abramowitz, M., Stegun, I.A. (eds.): Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series 55, 9th printing, Washington (1970)

2. Asmussen, S., Hobolth, A.: Markov bridges, bisection and variance reduction. In: Plaskota, L., Wozniakowski, H. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2010. Springer Proceedings in Mathematics and Statistics, vol. 23. Springer, Berlin (2012)

3. Bedini, M.L.: Information on a Default Time: Brownian Bridges on Stochastic Intervals and Enlargement of Filtrations. PhD Thesis, Friedrich Schiller University of Jena (Germany) (2012)

4. Bertoin, J.: Lévy Processes. Cambridge University Press, Cambridge (1996)

5. Bedini, M.L., Buckdahn, R., Engelbert, H.J.: Brownian bridges on random intervals. Theory Probab. Appl. 61(1), 15–39 (2017)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3