2015/09/17 by Bogso, Antoine Marie
#32F17 #60E15 #60G44 #60J25 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1509.05123
We use multivariate total positivity theory to exhibit new families of peacocks. As the authors of \citeHPRY, our guiding example is the result of Carr-Ewald-Xiao \citeCEX. We shall introduce the notion of strong conditional monotonicity. This concept is strictly more restrictive than the conditional monotonicity as defined in \citeHPRY (see also \citeBe, \citeBPR1 and \citeShS1). There are many random vectors which are strongly conditionally monotone (SCM). Indeed, we shall prove that multivariate totally positive of order 2 (MTP2) random vectors are SCM. As a consequence, stochastic processes with MTP2 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.