Inversion, duality and Doob $h$-transforms for self-similar Markov processes
نویسندگان
چکیده
منابع مشابه
Self-Similar Markov Processes on Cantor Set
We define analogues of Brownian motion on the triadic Cantor set by introducing a few natural requirements on the Markov semigroup. We give a detailed description of these symmetric self-similar processes and study their properties such as mixing and moment asymptotics.
متن کاملOn inversions and Doob h-transforms of linear diffusions
Let X be a regular linear diffusion whose state space is an open interval E ⊆ R. We consider a diffusion X∗ which probability law is obtained as a Doob htransform of the law of X, where h is a positive harmonic function for the infinitesimal generator of X on E. This is the dual of X with respect to h(x)m(dx) where m(dx) is the speed measure of X. Examples include the case where X∗ is X conditi...
متن کاملHyper-self-duality of Hamming and Doob graphs
We show that the Doob and Hamming graphs are hyper-self-dual. We then show that although the Doob graphs are formally dual to certain Hamming graphs, they are not hyper-dual to them. We do so by showing that Bose-Mesner subalgebras and Kronecker products of Bose-Mesner algebras inherit hyper-duality.
متن کاملDuality for Labelled Markov Processes
Labelled Markov processes (LMPs) are automata whose transitions are given by probability distributions. In this paper we present a ‘universal’ LMP as the spectrum of a commutative C∗-algebra consisting of formal linear combinations of labelled trees. We characterize the state space of the universal LMP as the set of homomorphims from an ordered commutative monoid of labelled trees into the mult...
متن کاملOptimal prediction for positive self-similar Markov processes
This paper addresses the question of predicting when a positive self-similar Markov process X attains its pathwise global supremum or infimum before hitting zero for the first time (if it does at all). This problem has been studied in [9] under the assumption that X is a positive transient diffusion. We extend their result to the class of positive self-similar Markov processes by establishing a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Probability
سال: 2017
ISSN: 1083-6489
DOI: 10.1214/17-ejp33