The Matsumoto–Yor property on trees
نویسندگان
چکیده
Viewing the Matsumoto–Yor property as a bivariate property with respect to the simple tree with two vertices and one edge, we extend it to a p-variate property with respect to any tree with p vertices. The converse of the Matsumoto–Yor property, which characterizes the product of a gamma and a generalized inverse Gaussian distribution, is extended to characterize the product of a gamma and p 1 generalized inverse Gaussian distributions. A striking feature of this characterization is that we need the independence of the components of random vectors corresponding only to the leaves of the tree. We illustrate our results with two particular trees: the two-link chain and the three-branch ‘daisy’.
منابع مشابه
Kummer and gamma laws through independences on trees - Another parallel with the Matsumoto-Yor property
متن کامل
On Azéma–yor Processes, Their Optimal Properties and the Bachelier–drawdown Equation *
We study the class of Azéma–Yor processes defined from a general semimartingale with a continuous running supremum process. We show that they arise as unique strong solutions of the Bachelier stochastic differential equation which we prove is equivalent to the Drawdown equation. Solutions of the latter have the drawdown property: they always stay above a given function of their past supremum. W...
متن کاملExponential functionals of Brownian motion, I: Probability laws at fixed time
This paper is the first part of our survey on various results about the distribution of exponential type Brownian functionals defined as an integral over time of geometric Brownian motion. Several related topics are also mentioned.
متن کاملConstructing self-similar martingales via two Skorokhod embeddings
With the help of two Skorokhod embeddings, we construct martingales which enjoy the Brownian scaling property and the (inhomogeneous) Markov property. The second method necessitates randomization, but allows to reach any law with finite moment of order 1, centered, as the distribution of such a martingale at unit time. The first method does not necessitate randomization, but an additional restr...
متن کاملFurther Exponential Generalization of Pitman’s 2m-x Theorem
We present a class of processes which enjoy an exponential analogue of Pitman’s 2M-X theorem, improving hence some works of H. Matsumoto and M. Yor.
متن کامل