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arXiv · 1509.05123

An application of multivariate total positivity to peacocks

Antoine Marie Bogso
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Abstract

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.

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Antoine Marie Bogso. 2015-09-17. An application of multivariate total positivity to peacocks. https://doi.org/10.1051/ps%2F2013049

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