818 research outputs found
Breadth first search coding of multitype forests with application to Lamperti representation
We obtain a bijection between some set of multidimensional sequences and this
of -type plane forests which is based on the breadth first search algorithm.
This coding sequence is related to the sequence of population sizes indexed by
the generations, through a Lamperti type transformation. The same
transformation in then obtained in continuous time for multitype branching
processes with discrete values. We show that any such process can be obtained
from a dimensional compound Poisson process time changed by some integral
functional. Our proof bears on the discretisation of branching forests with
edge lengths
La aglomeración urbana granadina y la transformación del paisaje del sector sur de la vega.
Sin resume
Large deviations for clocks of self-similar processes
The Lamperti correspondence gives a prominent role to two random time
changes: the exponential functional of a L\'evy process drifting to
and its inverse, the clock of the corresponding positive self-similar process.
We describe here asymptotical properties of these clocks in large time,
extending the results of Yor and Zani
Potentials of stable processes
For a stable process, we give an explicit formula for the potential measure
of the process killed outside a bounded interval and the joint law of the
overshoot, undershoot and undershoot from the maximum at exit from a bounded
interval. We obtain the equivalent quantities for a stable process reflected in
its infimum. The results are obtained by exploiting a simple connection with
the Lamperti representation and exit problems of stable processes.Comment: 10 page
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