Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes

Details Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes

2005-08-27

arxiv.org/abs/math/0508542v1

Periodica Mathematica Hungarica Vol. 50 (1-2), 2005, 47-60

Mathematics

Probability

12 pages, To appear in Periodica Mathematica Hungarica

Scientific paper

First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein-Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein-Uhlenbeck process. We also construct bridges derived from general multidimensional Ornstein-Uhlenbeck processes.

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