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Two-parameter MRL processes and associated submartingales. (arXiv:1807.05932v1 [math.PR])
来源于:arXiv
We use Madan-Yor's argument to construct associated submartingales to a class
of two-parameter processes that are ordered by the increasing convex dominance.
This class includes processes which have MTP$_2$ integrated survival functions.
We prove that the integrated survival function of an integrable two-parameter
process is MTP$_2$ if and only if it is TP$_2$ in each pair of arguments when
the remaining argument is fixed. This result can not be deduced from known
results since there are several two-parameter processes whose integrated
survival functions do not have interval support. The MTP$_2$ property of
certain MRL processes is useful to exhibit numerous other processes having the
same property. We mention that a two-parameter process ordered by the
increasing convex dominance is not necessarily associated to a two-parameter
submartingale. A counterexample has been provided recently by Juillet. 查看全文>>