An application of multivariate total positivity to peacocks

Bogso, Antoine-Marie

doi:10.1051/ps/2013049

Cited by 2 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There are many interesting Markov processes which admit a TP 2 transition kernel. For example, processes with independent and log-concave increments, absolute values of processes with independent and symmetric PF ∞ increments, birth-death processes, one-dimensional diffusions and the bridges of one-dimensional diffusions have a TP 2 transition kernel (see e.g., [3,10,12,11]). Now, we restrict our attention to R + -valued Markov processes which admit a TP 2 transition kernel.…”

Section: Log-concavity Properties Of Nonnegative Markov Processesmentioning

confidence: 99%

MRL order, log-concavity and an application to peacocks

Bogso

2015

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

Highlights• We recall some properties of R + -valued homogeneous Markov processes which admit a totally positive transition kernel.• We establish the equivalence between the MRL ordering and a log-concavity type condition.• We exhibit new classes of MRL processes, i.e. integrable processes which increase in the MRL order. AbstractWe provide an equivalent log-concavity condition to the mean residual life (MRL) ordering for realvalued processes. This result, combined with classical properties of total positivity of order 2, allows to exhibit new families of integrable processes which increase in the MRL order (MRL processes). Note that MRL processes with constant mean are peacocks to which the Azéma-Yor (Skorokhod embedding) algorithm yields an explicit associated martingale.

show abstract

Section: Log-concavity Properties Of Nonnegative Markov Processesmentioning

confidence: 99%

MRL order, log-concavity and an application to peacocks

Bogso

2015

Stochastic Processes and their Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Weak decreasing stochastic order

Bogso

Soh

2017

Statistics & Probability Letters

View full text Add to dashboard Cite

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.

show abstract

An application of multivariate total positivity to peacocks

Cited by 2 publications

References 29 publications

MRL order, log-concavity and an application to peacocks

MRL order, log-concavity and an application to peacocks

Weak decreasing stochastic order

Contact Info

Product

Resources

About