An application of multivariate total positivity to peacocks
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arXiv
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| Format: | Preprint |
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2015
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| _version_ | 1866912577034911744 |
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| author | Bogso, Antoine Marie |
| author_facet | Bogso, Antoine Marie |
| contents | We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of \cite{HPRY}, our guiding example is the result of Carr-Ewald-Xiao \cite{CEX}. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in \cite{HPRY} (see also \cite{Be}, \cite{BPR1} and \cite{ShS1}). There are many random vectors which are strongly conditionally monotone (SCM). Indeed, we shall prove that multivariate totally positive of order 2 (MTP$_2$) random vectors are SCM. As a consequence, stochastic processes with MTP$_2$ finite-dimensional marginals are SCM. This family includes processes with independent and log-concave increments, and one-dimensional diffusions which have absolutely continuous transition kernels. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1509_05123 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | An application of multivariate total positivity to peacocks Bogso, Antoine Marie Probability 60J25, 32F17, 60G44, 60E15 We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of \cite{HPRY}, our guiding example is the result of Carr-Ewald-Xiao \cite{CEX}. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in \cite{HPRY} (see also \cite{Be}, \cite{BPR1} and \cite{ShS1}). There are many random vectors which are strongly conditionally monotone (SCM). Indeed, we shall prove that multivariate totally positive of order 2 (MTP$_2$) random vectors are SCM. As a consequence, stochastic processes with MTP$_2$ finite-dimensional marginals are SCM. This family includes processes with independent and log-concave increments, and one-dimensional diffusions which have absolutely continuous transition kernels. |
| title | An application of multivariate total positivity to peacocks |
| topic | Probability 60J25, 32F17, 60G44, 60E15 |
| url | https://arxiv.org/abs/1509.05123 |