Weak decreasing stochastic order
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2016
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911143169097728 |
|---|---|
| author | Bogso, Antoine-Marie Soh, Patrice Takam |
| author_facet | Bogso, Antoine-Marie Soh, Patrice Takam |
| contents | We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan-Yor's argument, it follows that the WDS ordering is a necessary and sufficient condition for a process with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azéma-Yor algorithm. Since the decreasing stochastic order is stronger than the WDS order, then, for every stochastically non-decreasing family of probability measures with densities, the Cox-Hobson stopping times provide an associated Markov process. The quantile process associated to a stochastically non-decreasing process is not necessarily Markovian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1610_02190 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Weak decreasing stochastic order Bogso, Antoine-Marie Soh, Patrice Takam Probability 60E15, 60G44, 60J25 We introduce the notion of weak decreasing stochastic (WDS) ordering for real-valued processes with negative means, which, to our knowledge, has not been studied before. Thanks to Madan-Yor's argument, it follows that the WDS ordering is a necessary and sufficient condition for a process with negative mean to be embeddable in a standard Brownian motion by the Cox and Hobson extension of the Azéma-Yor algorithm. Since the decreasing stochastic order is stronger than the WDS order, then, for every stochastically non-decreasing family of probability measures with densities, the Cox-Hobson stopping times provide an associated Markov process. The quantile process associated to a stochastically non-decreasing process is not necessarily Markovian. |
| title | Weak decreasing stochastic order |
| topic | Probability 60E15, 60G44, 60J25 |
| url | https://arxiv.org/abs/1610.02190 |